-7k^2+10k+15=6

Solution for -7k^2+10k+15=6 equation:

-7k^2+10k+15=6

We move all terms to the left:

-7k^2+10k+15-(6)=0

We add all the numbers together, and all the variables

-7k^2+10k+9=0

a = -7; b = 10; c = +9;
Δ = b2-4ac
Δ = 102-4·(-7)·9
Δ = 352
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:

$\sqrt{\Delta}=\sqrt{352}=\sqrt{16*22}=\sqrt{16}*\sqrt{22}=4\sqrt{22}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-4\sqrt{22}}{2*-7}=\frac{-10-4\sqrt{22}}{-14}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4\sqrt{22}}{2*-7}=\frac{-10+4\sqrt{22}}{-14}
$