6k^2+4k-15=0

Solution for 6k^2+4k-15=0 equation:

6k^2+4k-15=0

a = 6; b = 4; c = -15;
Δ = b2-4ac
Δ = 42-4·6·(-15)
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{94}}{2*6}=\frac{-4-2\sqrt{94}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{94}}{2*6}=\frac{-4+2\sqrt{94}}{12}
$