27x^2+18x=360x-64

Solution for 27x^2+18x=360x-64 equation:

27x^2+18x=360x-64

We move all terms to the left:

27x^2+18x-(360x-64)=0

We get rid of parentheses

27x^2+18x-360x+64=0

We add all the numbers together, and all the variables

27x^2-342x+64=0

a = 27; b = -342; c = +64;
Δ = b2-4ac
Δ = -3422-4·27·64
Δ = 110052
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:

$\sqrt{\Delta}=\sqrt{110052}=\sqrt{36*3057}=\sqrt{36}*\sqrt{3057}=6\sqrt{3057}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-342)-6\sqrt{3057}}{2*27}=\frac{342-6\sqrt{3057}}{54}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-342)+6\sqrt{3057}}{2*27}=\frac{342+6\sqrt{3057}}{54}
$