10x^2-19x-117=0

Solution for 10x^2-19x-117=0 equation:

10x^2-19x-117=0

a = 10; b = -19; c = -117;
Δ = b2-4ac
Δ = -192-4·10·(-117)
Δ = 5041
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5041}=71$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-19)-71}{2*10}=\frac{-52}{20}
=-2+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-19)+71}{2*10}=\frac{90}{20}
=4+1/2
$