3k^2=11k-10

Solution for 3k^2=11k-10 equation:

3k^2=11k-10

We move all terms to the left:

3k^2-(11k-10)=0

We get rid of parentheses

3k^2-11k+10=0

a = 3; b = -11; c = +10;
Δ = b2-4ac
Δ = -112-4·3·10
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-1}{2*3}=\frac{10}{6}
=1+2/3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+1}{2*3}=\frac{12}{6}
=2
$