5x^2-67x-120=0

Solution for 5x^2-67x-120=0 equation:

5x^2-67x-120=0

a = 5; b = -67; c = -120;
Δ = b2-4ac
Δ = -672-4·5·(-120)
Δ = 6889
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6889}=83$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-67)-83}{2*5}=\frac{-16}{10}
=-1+3/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-67)+83}{2*5}=\frac{150}{10}
=15
$