3x^2-6x-23=3

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

3x^2-6x-23=3

We move all terms to the left:

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

We add all the numbers together, and all the variables

3x^2-6x-26=0

a = 3; b = -6; c = -26;
Δ = b2-4ac
Δ = -62-4·3·(-26)
Δ = 348
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:

$\sqrt{\Delta}=\sqrt{348}=\sqrt{4*87}=\sqrt{4}*\sqrt{87}=2\sqrt{87}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{87}}{2*3}=\frac{6-2\sqrt{87}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{87}}{2*3}=\frac{6+2\sqrt{87}}{6}
$