6k2+5k=80

Solution for 6k2+5k=80 equation:

6k^2+5k=80

We move all terms to the left:

6k^2+5k-(80)=0

a = 6; b = 5; c = -80;
Δ = b2-4ac
Δ = 52-4·6·(-80)
Δ = 1945
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-\sqrt{1945}}{2*6}=\frac{-5-\sqrt{1945}}{12}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+\sqrt{1945}}{2*6}=\frac{-5+\sqrt{1945}}{12}
$