8x=x^2-40

Solution for 8x=x^2-40 equation:

8x=x^2-40

We move all terms to the left:

8x-(x^2-40)=0

We get rid of parentheses

-x^2+8x+40=0

We add all the numbers together, and all the variables

-1x^2+8x+40=0

a = -1; b = 8; c = +40;
Δ = b2-4ac
Δ = 82-4·(-1)·40
Δ = 224
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:

$\sqrt{\Delta}=\sqrt{224}=\sqrt{16*14}=\sqrt{16}*\sqrt{14}=4\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-4\sqrt{14}}{2*-1}=\frac{-8-4\sqrt{14}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+4\sqrt{14}}{2*-1}=\frac{-8+4\sqrt{14}}{-2}
$