6r^2-4r=9

Solution for 6r^2-4r=9 equation:

6r^2-4r=9

We move all terms to the left:

6r^2-4r-(9)=0

a = 6; b = -4; c = -9;
Δ = b2-4ac
Δ = -42-4·6·(-9)
Δ = 232
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:

$\sqrt{\Delta}=\sqrt{232}=\sqrt{4*58}=\sqrt{4}*\sqrt{58}=2\sqrt{58}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{58}}{2*6}=\frac{4-2\sqrt{58}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{58}}{2*6}=\frac{4+2\sqrt{58}}{12}
$