4x-0,01x^2=120

Solution for 4x-0,01x^2=120 equation:

4x-0.01x^2=120

We move all terms to the left:

4x-0.01x^2-(120)=0

a = -0.01; b = 4; c = -120;
Δ = b2-4ac
Δ = 42-4·(-0.01)·(-120)
Δ = 11.2
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-\sqrt{11.2}}{2*-0.01}=\frac{-4-\sqrt{11.2}}{-0.02}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+\sqrt{11.2}}{2*-0.01}=\frac{-4+\sqrt{11.2}}{-0.02}
$