14k^2=30+23k

Solution for 14k^2=30+23k equation:

14k^2=30+23k

We move all terms to the left:

14k^2-(30+23k)=0

We add all the numbers together, and all the variables

14k^2-(23k+30)=0

We get rid of parentheses

14k^2-23k-30=0

a = 14; b = -23; c = -30;
Δ = b2-4ac
Δ = -232-4·14·(-30)
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-47}{2*14}=\frac{-24}{28}
=-6/7
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+47}{2*14}=\frac{70}{28}
=2+1/2
$