6x^2+31x+39=0

Solution for 6x^2+31x+39=0 equation:

6x^2+31x+39=0

a = 6; b = 31; c = +39;
Δ = b2-4ac
Δ = 312-4·6·39
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-5}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+5}{2*6}=\frac{-26}{12}
=-2+1/6
$