2x+18=6x2-2

Solution for 2x+18=6x2-2 equation:

2x+18=6x^2-2

We move all terms to the left:

2x+18-(6x^2-2)=0

We get rid of parentheses

-6x^2+2x+2+18=0

We add all the numbers together, and all the variables

-6x^2+2x+20=0

a = -6; b = 2; c = +20;
Δ = b2-4ac
Δ = 22-4·(-6)·20
Δ = 484
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{484}=22$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-22}{2*-6}=\frac{-24}{-12}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+22}{2*-6}=\frac{20}{-12}
=-1+2/3
$