x=3x^2+48x-324

Solution for x=3x^2+48x-324 equation:

x=3x^2+48x-324

We move all terms to the left:

x-(3x^2+48x-324)=0

We get rid of parentheses

-3x^2+x-48x+324=0

We add all the numbers together, and all the variables

-3x^2-47x+324=0

a = -3; b = -47; c = +324;
Δ = b2-4ac
Δ = -472-4·(-3)·324
Δ = 6097
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-47)-\sqrt{6097}}{2*-3}=\frac{47-\sqrt{6097}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-47)+\sqrt{6097}}{2*-3}=\frac{47+\sqrt{6097}}{-6}
$