108x^2+27x-36x-9-36x^2-18x-36x-12=54x^2+36x+24-45x+15

Solution for 108x^2+27x-36x-9-36x^2-18x-36x-12=54x^2+36x+24-45x+15 equation:

108x^2+27x-36x-9-36x^2-18x-36x-12=54x^2+36x+24-45x+15

We move all terms to the left:

108x^2+27x-36x-9-36x^2-18x-36x-12-(54x^2+36x+24-45x+15)=0

We add all the numbers together, and all the variables

72x^2-63x-(54x^2+36x+24-45x+15)-21=0

We get rid of parentheses

72x^2-54x^2-63x-36x+45x-24-15-21=0

We add all the numbers together, and all the variables

18x^2-54x-60=0

a = 18; b = -54; c = -60;
Δ = b2-4ac
Δ = -542-4·18·(-60)
Δ = 7236
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{7236}=\sqrt{36*201}=\sqrt{36}*\sqrt{201}=6\sqrt{201}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-6\sqrt{201}}{2*18}=\frac{54-6\sqrt{201}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+6\sqrt{201}}{2*18}=\frac{54+6\sqrt{201}}{36}
$