4x^2+30x-117=0

Solution for 4x^2+30x-117=0 equation:

4x^2+30x-117=0

a = 4; b = 30; c = -117;
Δ = b2-4ac
Δ = 302-4·4·(-117)
Δ = 2772
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:

$\sqrt{\Delta}=\sqrt{2772}=\sqrt{36*77}=\sqrt{36}*\sqrt{77}=6\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{77}}{2*4}=\frac{-30-6\sqrt{77}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{77}}{2*4}=\frac{-30+6\sqrt{77}}{8}
$