-0.04x^2=4.2x+11.8

Solution for -0.04x^2=4.2x+11.8 equation:

-0.04x^2=4.2x+11.8

We move all terms to the left:

-0.04x^2-(4.2x+11.8)=0

We get rid of parentheses

-0.04x^2-4.2x-11.8=0

a = -0.04; b = -4.2; c = -11.8;
Δ = b2-4ac
Δ = -4.22-4·(-0.04)·(-11.8)
Δ = 15.752
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{-(-4.2)-\sqrt{15.752}}{2*-0.04}=\frac{4.2-\sqrt{15.752}}{-0.08}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4.2)+\sqrt{15.752}}{2*-0.04}=\frac{4.2+\sqrt{15.752}}{-0.08}
$