7k=-3k^2+3

Solution for 7k=-3k^2+3 equation:

7k=-3k^2+3

We move all terms to the left:

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

We get rid of parentheses

3k^2+7k-3=0

a = 3; b = 7; c = -3;
Δ = b2-4ac
Δ = 72-4·3·(-3)
Δ = 85
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{85}}{2*3}=\frac{-7-\sqrt{85}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{85}}{2*3}=\frac{-7+\sqrt{85}}{6}
$