85=0.2313x^2+2.600x+35.17

Solution for 85=0.2313x^2+2.600x+35.17 equation:

85=0.2313x^2+2.600x+35.17

We move all terms to the left:

85-(0.2313x^2+2.600x+35.17)=0

We get rid of parentheses

-0.2313x^2-2.600x-35.17+85=0

We add all the numbers together, and all the variables

-0.2313x^2-2.6x+49.83=0

a = -0.2313; b = -2.6; c = +49.83;
Δ = b2-4ac
Δ = -2.62-4·(-0.2313)·49.83
Δ = 52.862716
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{-(-2.6)-\sqrt{52.862716}}{2*-0.2313}=\frac{2.6-\sqrt{52.862716}}{-0.4626}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2.6)+\sqrt{52.862716}}{2*-0.2313}=\frac{2.6+\sqrt{52.862716}}{-0.4626}
$