7k^2+12=-31k

Solution for 7k^2+12=-31k equation:

7k^2+12=-31k

We move all terms to the left:

7k^2+12-(-31k)=0

We get rid of parentheses

7k^2+31k+12=0

a = 7; b = 31; c = +12;
Δ = b2-4ac
Δ = 312-4·7·12
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31)-25}{2*7}=\frac{-56}{14}
=-4
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+25}{2*7}=\frac{-6}{14}
=-3/7
$