6a^2-4a-30=0

Solution for 6a^2-4a-30=0 equation:

6a^2-4a-30=0

a = 6; b = -4; c = -30;
Δ = b2-4ac
Δ = -42-4·6·(-30)
Δ = 736
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{46}}{2*6}=\frac{4-4\sqrt{46}}{12}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{46}}{2*6}=\frac{4+4\sqrt{46}}{12}
$