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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

6r^2-23r-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:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-25}{2*6}=\frac{-2}{12}
=-1/6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+25}{2*6}=\frac{48}{12}
=4
$