18x^2-30x-3=9x+12

Solution for 18x^2-30x-3=9x+12 equation:

18x^2-30x-3=9x+12

We move all terms to the left:

18x^2-30x-3-(9x+12)=0

We get rid of parentheses

18x^2-30x-9x-12-3=0

We add all the numbers together, and all the variables

18x^2-39x-15=0

a = 18; b = -39; c = -15;
Δ = b2-4ac
Δ = -392-4·18·(-15)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-51}{2*18}=\frac{-12}{36}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+51}{2*18}=\frac{90}{36}
=2+1/2
$