6x^2-17x-39=0

Solution for 6x^2-17x-39=0 equation:

6x^2-17x-39=0

a = 6; b = -17; c = -39;
Δ = b2-4ac
Δ = -172-4·6·(-39)
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-35}{2*6}=\frac{-18}{12}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+35}{2*6}=\frac{52}{12}
=4+1/3
$