108x^2+33x-30=0

Solution for 108x^2+33x-30=0 equation:

108x^2+33x-30=0

a = 108; b = 33; c = -30;
Δ = b2-4ac
Δ = 332-4·108·(-30)
Δ = 14049
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{14049}=\sqrt{9*1561}=\sqrt{9}*\sqrt{1561}=3\sqrt{1561}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-3\sqrt{1561}}{2*108}=\frac{-33-3\sqrt{1561}}{216}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+3\sqrt{1561}}{2*108}=\frac{-33+3\sqrt{1561}}{216}
$