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

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

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

We move all terms to the left:

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

We get rid of parentheses

-3x^2-9x+x+30=0

We add all the numbers together, and all the variables

-3x^2-8x+30=0

a = -3; b = -8; c = +30;
Δ = b2-4ac
Δ = -82-4·(-3)·30
Δ = 424
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:

$\sqrt{\Delta}=\sqrt{424}=\sqrt{4*106}=\sqrt{4}*\sqrt{106}=2\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{106}}{2*-3}=\frac{8-2\sqrt{106}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{106}}{2*-3}=\frac{8+2\sqrt{106}}{-6}
$