x^2-40x=20000

Solution for x^2-40x=20000 equation:

x^2-40x=20000

We move all terms to the left:

x^2-40x-(20000)=0

a = 1; b = -40; c = -20000;
Δ = b2-4ac
Δ = -402-4·1·(-20000)
Δ = 81600
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:

$\sqrt{\Delta}=\sqrt{81600}=\sqrt{1600*51}=\sqrt{1600}*\sqrt{51}=40\sqrt{51}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-40\sqrt{51}}{2*1}=\frac{40-40\sqrt{51}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+40\sqrt{51}}{2*1}=\frac{40+40\sqrt{51}}{2}
$