X2-40x=1500

Solution for X2-40x=1500 equation:

X2-40X=1500

We move all terms to the left:

X2-40X-(1500)=0

We add all the numbers together, and all the variables

X^2-40X-1500=0

a = 1; b = -40; c = -1500;
Δ = b2-4ac
Δ = -402-4·1·(-1500)
Δ = 7600
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:

$\sqrt{\Delta}=\sqrt{7600}=\sqrt{400*19}=\sqrt{400}*\sqrt{19}=20\sqrt{19}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-20\sqrt{19}}{2*1}=\frac{40-20\sqrt{19}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+20\sqrt{19}}{2*1}=\frac{40+20\sqrt{19}}{2}
$