6x^2-23x-9=-5

Solution for 6x^2-23x-9=-5 equation:

6x^2-23x-9=-5

We move all terms to the left:

6x^2-23x-9-(-5)=0

We add all the numbers together, and all the variables

6x^2-23x-4=0

a = 6; b = -23; c = -4;
Δ = b2-4ac
Δ = -232-4·6·(-4)
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*6}=\frac{-2}{12}
=-1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*6}=\frac{48}{12}
=4
$