9x+18=2x^2+3x-2

Solution for 9x+18=2x^2+3x-2 equation:

9x+18=2x^2+3x-2

We move all terms to the left:

9x+18-(2x^2+3x-2)=0

We get rid of parentheses

-2x^2+9x-3x+2+18=0

We add all the numbers together, and all the variables

-2x^2+6x+20=0

a = -2; b = 6; c = +20;
Δ = b2-4ac
Δ = 62-4·(-2)·20
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-14}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+14}{2*-2}=\frac{8}{-4}
=-2
$