-2x^2+100x=600

Solution for -2x^2+100x=600 equation:

-2x^2+100x=600

We move all terms to the left:

-2x^2+100x-(600)=0

a = -2; b = 100; c = -600;
Δ = b2-4ac
Δ = 1002-4·(-2)·(-600)
Δ = 5200
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:

$\sqrt{\Delta}=\sqrt{5200}=\sqrt{400*13}=\sqrt{400}*\sqrt{13}=20\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(100)-20\sqrt{13}}{2*-2}=\frac{-100-20\sqrt{13}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(100)+20\sqrt{13}}{2*-2}=\frac{-100+20\sqrt{13}}{-4}
$