2x^2+5x=3x^2-2x-18

Solution for 2x^2+5x=3x^2-2x-18 equation:

2x^2+5x=3x^2-2x-18

We move all terms to the left:

2x^2+5x-(3x^2-2x-18)=0

We get rid of parentheses

2x^2-3x^2+5x+2x+18=0

We add all the numbers together, and all the variables

-1x^2+7x+18=0

a = -1; b = 7; c = +18;
Δ = b2-4ac
Δ = 72-4·(-1)·18
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*-1}=\frac{-18}{-2}
=+9
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*-1}=\frac{4}{-2}
=-2
$