6r^2-15r-6=0

Solution for 6r^2-15r-6=0 equation:

6r^2-15r-6=0

a = 6; b = -15; c = -6;
Δ = b2-4ac
Δ = -152-4·6·(-6)
Δ = 369
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:

$\sqrt{\Delta}=\sqrt{369}=\sqrt{9*41}=\sqrt{9}*\sqrt{41}=3\sqrt{41}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-3\sqrt{41}}{2*6}=\frac{15-3\sqrt{41}}{12}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+3\sqrt{41}}{2*6}=\frac{15+3\sqrt{41}}{12}
$