6x2+39x=60

Solution for 6x2+39x=60 equation:

6x^2+39x=60

We move all terms to the left:

6x^2+39x-(60)=0

a = 6; b = 39; c = -60;
Δ = b2-4ac
Δ = 392-4·6·(-60)
Δ = 2961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2961}=\sqrt{9*329}=\sqrt{9}*\sqrt{329}=3\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(39)-3\sqrt{329}}{2*6}=\frac{-39-3\sqrt{329}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(39)+3\sqrt{329}}{2*6}=\frac{-39+3\sqrt{329}}{12}
$