80x-4x^2=200

Solution for 80x-4x^2=200 equation:

80x-4x^2=200

We move all terms to the left:

80x-4x^2-(200)=0

a = -4; b = 80; c = -200;
Δ = b2-4ac
Δ = 802-4·(-4)·(-200)
Δ = 3200
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:

$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-40\sqrt{2}}{2*-4}=\frac{-80-40\sqrt{2}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+40\sqrt{2}}{2*-4}=\frac{-80+40\sqrt{2}}{-8}
$