0.85x^2+12.5x=500

Solution for 0.85x^2+12.5x=500 equation:

0.85x^2+12.5x=500

We move all terms to the left:

0.85x^2+12.5x-(500)=0

a = 0.85; b = 12.5; c = -500;
Δ = b2-4ac
Δ = 12.52-4·0.85·(-500)
Δ = 1856.25
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{-(12.5)-\sqrt{1856.25}}{2*0.85}=\frac{-12.5-\sqrt{1856.25}}{1.7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12.5)+\sqrt{1856.25}}{2*0.85}=\frac{-12.5+\sqrt{1856.25}}{1.7}
$