6x2+5x=39

Solution for 6x2+5x=39 equation:

6x^2+5x=39

We move all terms to the left:

6x^2+5x-(39)=0

a = 6; b = 5; c = -39;
Δ = b2-4ac
Δ = 52-4·6·(-39)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-31}{2*6}=\frac{-36}{12}
=-3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+31}{2*6}=\frac{26}{12}
=2+1/6
$