-27+3x+2x^2=27x+18

Solution for -27+3x+2x^2=27x+18 equation:

-27+3x+2x^2=27x+18

We move all terms to the left:

-27+3x+2x^2-(27x+18)=0

We get rid of parentheses

2x^2+3x-27x-18-27=0

We add all the numbers together, and all the variables

2x^2-24x-45=0

a = 2; b = -24; c = -45;
Δ = b2-4ac
Δ = -242-4·2·(-45)
Δ = 936
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:

$\sqrt{\Delta}=\sqrt{936}=\sqrt{36*26}=\sqrt{36}*\sqrt{26}=6\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-6\sqrt{26}}{2*2}=\frac{24-6\sqrt{26}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+6\sqrt{26}}{2*2}=\frac{24+6\sqrt{26}}{4}
$