5x^2-32X=-8

Solution for 5x^2-32X=-8 equation:

5x^2-32x=-8

We move all terms to the left:

5x^2-32x-(-8)=0

We add all the numbers together, and all the variables

5x^2-32x+8=0

a = 5; b = -32; c = +8;
Δ = b2-4ac
Δ = -322-4·5·8
Δ = 864
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:

$\sqrt{\Delta}=\sqrt{864}=\sqrt{144*6}=\sqrt{144}*\sqrt{6}=12\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-12\sqrt{6}}{2*5}=\frac{32-12\sqrt{6}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+12\sqrt{6}}{2*5}=\frac{32+12\sqrt{6}}{10}
$