6k^2+84k=288

Solution for 6k^2+84k=288 equation:

6k^2+84k=288

We move all terms to the left:

6k^2+84k-(288)=0

a = 6; b = 84; c = -288;
Δ = b2-4ac
Δ = 842-4·6·(-288)
Δ = 13968
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{13968}=\sqrt{144*97}=\sqrt{144}*\sqrt{97}=12\sqrt{97}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-12\sqrt{97}}{2*6}=\frac{-84-12\sqrt{97}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+12\sqrt{97}}{2*6}=\frac{-84+12\sqrt{97}}{12}
$