X^2+30*x-117=0

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

X^2+30X-117=0

a = 1; b = 30; c = -117;
Δ = b2-4ac
Δ = 302-4·1·(-117)
Δ = 1368
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:

$\sqrt{\Delta}=\sqrt{1368}=\sqrt{36*38}=\sqrt{36}*\sqrt{38}=6\sqrt{38}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-6\sqrt{38}}{2*1}=\frac{-30-6\sqrt{38}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+6\sqrt{38}}{2*1}=\frac{-30+6\sqrt{38}}{2}
$