-0.08*x^2-0.5*x+67=52.38

Solution for -0.08*x^2-0.5*x+67=52.38 equation:

-0.08x^2-0.5x+67=52.38

We move all terms to the left:

-0.08x^2-0.5x+67-(52.38)=0

We add all the numbers together, and all the variables

-0.08x^2-0.5x+14.62=0

a = -0.08; b = -0.5; c = +14.62;
Δ = b2-4ac
Δ = -0.52-4·(-0.08)·14.62
Δ = 4.9284
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{-(-0.5)-\sqrt{4.9284}}{2*-0.08}=\frac{0.5-\sqrt{4.9284}}{-0.16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-0.5)+\sqrt{4.9284}}{2*-0.08}=\frac{0.5+\sqrt{4.9284}}{-0.16}
$