60x-2x^2=200

Solution for 60x-2x^2=200 equation:

60x-2x^2=200

We move all terms to the left:

60x-2x^2-(200)=0

a = -2; b = 60; c = -200;
Δ = b2-4ac
Δ = 602-4·(-2)·(-200)
Δ = 2000
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:

$\sqrt{\Delta}=\sqrt{2000}=\sqrt{400*5}=\sqrt{400}*\sqrt{5}=20\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{5}}{2*-2}=\frac{-60-20\sqrt{5}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{5}}{2*-2}=\frac{-60+20\sqrt{5}}{-4}
$