6r^2+12r-23=2

Solution for 6r^2+12r-23=2 equation:

6r^2+12r-23=2

We move all terms to the left:

6r^2+12r-23-(2)=0

We add all the numbers together, and all the variables

6r^2+12r-25=0

a = 6; b = 12; c = -25;
Δ = b2-4ac
Δ = 122-4·6·(-25)
Δ = 744
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{744}=\sqrt{4*186}=\sqrt{4}*\sqrt{186}=2\sqrt{186}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-2\sqrt{186}}{2*6}=\frac{-12-2\sqrt{186}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+2\sqrt{186}}{2*6}=\frac{-12+2\sqrt{186}}{12}
$