-2x^2+1000x=80000

Solution for -2x^2+1000x=80000 equation:

-2x^2+1000x=80000

We move all terms to the left:

-2x^2+1000x-(80000)=0

a = -2; b = 1000; c = -80000;
Δ = b2-4ac
Δ = 10002-4·(-2)·(-80000)
Δ = 360000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{360000}=600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1000)-600}{2*-2}=\frac{-1600}{-4}
=+400
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1000)+600}{2*-2}=\frac{-400}{-4}
=+100
$