3k(2k+7)=15

Solution for 3k(2k+7)=15 equation:

3k(2k+7)=15

We move all terms to the left:

3k(2k+7)-(15)=0

We multiply parentheses

6k^2+21k-15=0

a = 6; b = 21; c = -15;
Δ = b2-4ac
Δ = 212-4·6·(-15)
Δ = 801
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:

$\sqrt{\Delta}=\sqrt{801}=\sqrt{9*89}=\sqrt{9}*\sqrt{89}=3\sqrt{89}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-3\sqrt{89}}{2*6}=\frac{-21-3\sqrt{89}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+3\sqrt{89}}{2*6}=\frac{-21+3\sqrt{89}}{12}
$