60x-3x^2-100=0

Solution for 60x-3x^2-100=0 equation:

60x-3x^2-100=0

a = -3; b = 60; c = -100;
Δ = b2-4ac
Δ = 602-4·(-3)·(-100)
Δ = 2400
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:

$\sqrt{\Delta}=\sqrt{2400}=\sqrt{400*6}=\sqrt{400}*\sqrt{6}=20\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-20\sqrt{6}}{2*-3}=\frac{-60-20\sqrt{6}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+20\sqrt{6}}{2*-3}=\frac{-60+20\sqrt{6}}{-6}
$