2x^2-20x=1500

Solution for 2x^2-20x=1500 equation:

2x^2-20x=1500

We move all terms to the left:

2x^2-20x-(1500)=0

a = 2; b = -20; c = -1500;
Δ = b2-4ac
Δ = -202-4·2·(-1500)
Δ = 12400
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:

$\sqrt{\Delta}=\sqrt{12400}=\sqrt{400*31}=\sqrt{400}*\sqrt{31}=20\sqrt{31}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-20\sqrt{31}}{2*2}=\frac{20-20\sqrt{31}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+20\sqrt{31}}{2*2}=\frac{20+20\sqrt{31}}{4}
$