3x^2-6=23x+2

Solution for 3x^2-6=23x+2 equation:

3x^2-6=23x+2

We move all terms to the left:

3x^2-6-(23x+2)=0

We get rid of parentheses

3x^2-23x-2-6=0

We add all the numbers together, and all the variables

3x^2-23x-8=0

a = 3; b = -23; c = -8;
Δ = b2-4ac
Δ = -232-4·3·(-8)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-25}{2*3}=\frac{-2}{6}
=-1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*3}=\frac{48}{6}
=8
$