12k^2+10k=9

Solution for 12k^2+10k=9 equation:

12k^2+10k=9

We move all terms to the left:

12k^2+10k-(9)=0

a = 12; b = 10; c = -9;
Δ = b2-4ac
Δ = 102-4·12·(-9)
Δ = 532
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:

$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{133}}{2*12}=\frac{-10-2\sqrt{133}}{24}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{133}}{2*12}=\frac{-10+2\sqrt{133}}{24}
$