2r^2=-13r-6

Solution for 2r^2=-13r-6 equation:

2r^2=-13r-6

We move all terms to the left:

2r^2-(-13r-6)=0

We get rid of parentheses

2r^2+13r+6=0

a = 2; b = 13; c = +6;
Δ = b2-4ac
Δ = 132-4·2·6
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-11}{2*2}=\frac{-24}{4}
=-6
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+11}{2*2}=\frac{-2}{4}
=-1/2
$