7(k)=3k^2-7

Solution for 7(k)=3k^2-7 equation:

7(k)=3k^2-7

We move all terms to the left:

7(k)-(3k^2-7)=0

We get rid of parentheses

-3k^2+7k+7=0

a = -3; b = 7; c = +7;
Δ = b2-4ac
Δ = 72-4·(-3)·7
Δ = 133
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{-(7)-\sqrt{133}}{2*-3}=\frac{-7-\sqrt{133}}{-6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{133}}{2*-3}=\frac{-7+\sqrt{133}}{-6}
$