18521=0.17x^2-89.76x+17976.32

Solution for 18521=0.17x^2-89.76x+17976.32 equation:

18521=0.17x^2-89.76x+17976.32

We move all terms to the left:

18521-(0.17x^2-89.76x+17976.32)=0

We get rid of parentheses

-0.17x^2+89.76x-17976.32+18521=0

We add all the numbers together, and all the variables

-0.17x^2+89.76x+544.68=0

a = -0.17; b = 89.76; c = +544.68;
Δ = b2-4ac
Δ = 89.762-4·(-0.17)·544.68
Δ = 8427.24
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{-(89.76)-\sqrt{8427.24}}{2*-0.17}=\frac{-89.76-\sqrt{8427.24}}{-0.34}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(89.76)+\sqrt{8427.24}}{2*-0.17}=\frac{-89.76+\sqrt{8427.24}}{-0.34}
$