15k^2+15k=200

Solution for 15k^2+15k=200 equation:

15k^2+15k=200

We move all terms to the left:

15k^2+15k-(200)=0

a = 15; b = 15; c = -200;
Δ = b2-4ac
Δ = 152-4·15·(-200)
Δ = 12225
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:

$\sqrt{\Delta}=\sqrt{12225}=\sqrt{25*489}=\sqrt{25}*\sqrt{489}=5\sqrt{489}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(15)-5\sqrt{489}}{2*15}=\frac{-15-5\sqrt{489}}{30}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+5\sqrt{489}}{2*15}=\frac{-15+5\sqrt{489}}{30}
$