36k^2+51k-1=7

Solution for 36k^2+51k-1=7 equation:

36k^2+51k-1=7

We move all terms to the left:

36k^2+51k-1-(7)=0

We add all the numbers together, and all the variables

36k^2+51k-8=0

a = 36; b = 51; c = -8;
Δ = b2-4ac
Δ = 512-4·36·(-8)
Δ = 3753
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:

$\sqrt{\Delta}=\sqrt{3753}=\sqrt{9*417}=\sqrt{9}*\sqrt{417}=3\sqrt{417}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-3\sqrt{417}}{2*36}=\frac{-51-3\sqrt{417}}{72}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+3\sqrt{417}}{2*36}=\frac{-51+3\sqrt{417}}{72}
$