3k^2-8k=10

Solution for 3k^2-8k=10 equation:

3k^2-8k=10

We move all terms to the left:

3k^2-8k-(10)=0

a = 3; b = -8; c = -10;
Δ = b2-4ac
Δ = -82-4·3·(-10)
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{-(-8)-2\sqrt{46}}{2*3}=\frac{8-2\sqrt{46}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{46}}{2*3}=\frac{8+2\sqrt{46}}{6}
$