6X^2+15x=84

Solution for 6X^2+15x=84 equation:

6X^2+15X=84

We move all terms to the left:

6X^2+15X-(84)=0

a = 6; b = 15; c = -84;
Δ = b2-4ac
Δ = 152-4·6·(-84)
Δ = 2241
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:

$\sqrt{\Delta}=\sqrt{2241}=\sqrt{9*249}=\sqrt{9}*\sqrt{249}=3\sqrt{249}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-3\sqrt{249}}{2*6}=\frac{-15-3\sqrt{249}}{12}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+3\sqrt{249}}{2*6}=\frac{-15+3\sqrt{249}}{12}
$