5k^2=6k+8

Solution for 5k^2=6k+8 equation:

5k^2=6k+8

We move all terms to the left:

5k^2-(6k+8)=0

We get rid of parentheses

5k^2-6k-8=0

a = 5; b = -6; c = -8;
Δ = b2-4ac
Δ = -62-4·5·(-8)
Δ = 196
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{196}=14$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-14}{2*5}=\frac{-8}{10}
=-4/5
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+14}{2*5}=\frac{20}{10}
=2
$