5k^2+29k=6

Solution for 5k^2+29k=6 equation:

5k^2+29k=6

We move all terms to the left:

5k^2+29k-(6)=0

a = 5; b = 29; c = -6;
Δ = b2-4ac
Δ = 292-4·5·(-6)
Δ = 961
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{961}=31$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-31}{2*5}=\frac{-60}{10}
=-6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+31}{2*5}=\frac{2}{10}
=1/5
$