8=8x^2-38x+20

Solution for 8=8x^2-38x+20 equation:

8=8x^2-38x+20

We move all terms to the left:

8-(8x^2-38x+20)=0

We get rid of parentheses

-8x^2+38x-20+8=0

We add all the numbers together, and all the variables

-8x^2+38x-12=0

a = -8; b = 38; c = -12;
Δ = b2-4ac
Δ = 382-4·(-8)·(-12)
Δ = 1060
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:

$\sqrt{\Delta}=\sqrt{1060}=\sqrt{4*265}=\sqrt{4}*\sqrt{265}=2\sqrt{265}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-2\sqrt{265}}{2*-8}=\frac{-38-2\sqrt{265}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+2\sqrt{265}}{2*-8}=\frac{-38+2\sqrt{265}}{-16}
$