10x^2-23x-120=0

Solution for 10x^2-23x-120=0 equation:

10x^2-23x-120=0

a = 10; b = -23; c = -120;
Δ = b2-4ac
Δ = -232-4·10·(-120)
Δ = 5329
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5329}=73$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-73}{2*10}=\frac{-50}{20}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+73}{2*10}=\frac{96}{20}
=4+4/5
$