6x^2-31x-105=0

Solution for 6x^2-31x-105=0 equation:

6x^2-31x-105=0

a = 6; b = -31; c = -105;
Δ = b2-4ac
Δ = -312-4·6·(-105)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-31)-59}{2*6}=\frac{-28}{12}
=-2+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+59}{2*6}=\frac{90}{12}
=7+1/2
$