6r2+11r=30

Solution for 6r2+11r=30 equation:

6r^2+11r=30

We move all terms to the left:

6r^2+11r-(30)=0

a = 6; b = 11; c = -30;
Δ = b2-4ac
Δ = 112-4·6·(-30)
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-29}{2*6}=\frac{-40}{12}
=-3+1/3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+29}{2*6}=\frac{18}{12}
=1+1/2
$