x^2-8x=40

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

x^2-8x=40

We move all terms to the left:

x^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}
$