X2+3x-117=0

Solution for X2+3x-117=0 equation:

X2+3X-117=0

We add all the numbers together, and all the variables

X^2+3X-117=0

a = 1; b = 3; c = -117;
Δ = b2-4ac
Δ = 32-4·1·(-117)
Δ = 477
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:

$\sqrt{\Delta}=\sqrt{477}=\sqrt{9*53}=\sqrt{9}*\sqrt{53}=3\sqrt{53}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-3\sqrt{53}}{2*1}=\frac{-3-3\sqrt{53}}{2}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+3\sqrt{53}}{2*1}=\frac{-3+3\sqrt{53}}{2}
$