18=9x+2x^2

Solution for 18=9x+2x^2 equation:

18=9x+2x^2

We move all terms to the left:

18-(9x+2x^2)=0

We get rid of parentheses

-2x^2-9x+18=0

a = -2; b = -9; c = +18;
Δ = b2-4ac
Δ = -92-4·(-2)·18
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-15}{2*-2}=\frac{-6}{-4}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+15}{2*-2}=\frac{24}{-4}
=-6
$