5k^2=12k+2

Solution for 5k^2=12k+2 equation:

5k^2=12k+2

We move all terms to the left:

5k^2-(12k+2)=0

We get rid of parentheses

5k^2-12k-2=0

a = 5; b = -12; c = -2;
Δ = b2-4ac
Δ = -122-4·5·(-2)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{46}}{2*5}=\frac{12-2\sqrt{46}}{10}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{46}}{2*5}=\frac{12+2\sqrt{46}}{10}
$