3x^2+12x-231=x

Solution for 3x^2+12x-231=x equation:

3x^2+12x-231=x

We move all terms to the left:

3x^2+12x-231-(x)=0

We add all the numbers together, and all the variables

3x^2+11x-231=0

a = 3; b = 11; c = -231;
Δ = b2-4ac
Δ = 112-4·3·(-231)
Δ = 2893
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{-(11)-\sqrt{2893}}{2*3}=\frac{-11-\sqrt{2893}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{2893}}{2*3}=\frac{-11+\sqrt{2893}}{6}
$