The first one
Step-by-step explanation:
We want to find the roots of the equation -2x + 3 = -8x²
Step 1: Our first step is to get the equation in quadratic form so we can use the quadratic formula to find the roots
Quadratic form: ax² + bx + c = 0
We can easily get this equation in quadratic form by moving -8x² to the right side. We can do this using inverse operations. The inverse of subtraction is addition so to get rid of -8x² we add 8x² to both sides
After adding -8x² to both sides we acquire 8x² - 2x + 3 = 0
The equation is now in quadratic form meaning we can now use the quadratic formula to find the roots.
Quadratic Formula : 
where the values of a, b and c are derived from the equation
Remember that the equation is in quadratic form ax² + bx + c = 0
8x² - 2x + 3 = 0 so a = 8 , b = - 2 and c = 3
We then plug in these values into the quadratic formula ( note that the +- means plus or minus meaning that we have to evaluate this twice, once when the discriminant ( b² - 4(a)(c) is the discriminant ) is being add to -b and once when the discriminant is being subtracted from -b )
First lets evaluate when the discriminant is being added to -b
Recall the quadratic formula : 
a = 8 , b = - 2 and c = 3
Work being done inside of the square root: 2² = 4 , -4 * 8 = -32 , -32 * 3 = -96
4 - 96 = - 92
Work being done at denominator : 2 * 8 = 16
The first root is
We now do this same process but instead we subtract the discriminant.
We would be left with the same thing but it would be 
instead of
In some cases we would get a completely different answer, so evaluating it twice, once when the discriminant is being add to -b and once when the discriminant is being subtracted from -b may be important in some cases.
We then simplify the two roots. You may notice that there is a negative number under the radical and you might ask how can you square root a negative? well you can't which is when imaginary roots come in. Imaginary roots: i = -1 . We can take out an i from -92 making it 92 because i = -1 and -92/-1 = 92. We would be left with i√92
So we can conclude that the roots of the equation are 
Looking at the answer choices we notice that there are two very similar answers. The first and second one. The only difference between the two is that 2 is positive on the first one and 2 is negative on the second one. Looking at the roots we just found, the 2 should be positive therefore the answer is the first one.
Note that ± means plus or minus and it means that the expression can either be added or subtracted and it will be a root. This means that saying the roots are 
is the same as saying the roots are
