32=8X2-d

Solution for 32=8X2-d equation:

32=8X^2-X

We move all terms to the left:

32-(8X^2-X)=0

We get rid of parentheses

-8X^2+X+32=0

a = -8; b = 1; c = +32;
Δ = b2-4ac
Δ = 12-4·(-8)·32
Δ = 1025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{1025}=\sqrt{25*41}=\sqrt{25}*\sqrt{41}=5\sqrt{41}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-5\sqrt{41}}{2*-8}=\frac{-1-5\sqrt{41}}{-16}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+5\sqrt{41}}{2*-8}=\frac{-1+5\sqrt{41}}{-16}
$