7k^2-12=-40k

Solution for 7k^2-12=-40k equation:

7k^2-12=-40k

We move all terms to the left:

7k^2-12-(-40k)=0

We get rid of parentheses

7k^2+40k-12=0

a = 7; b = 40; c = -12;
Δ = b2-4ac
Δ = 402-4·7·(-12)
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-44}{2*7}=\frac{-84}{14}
=-6
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+44}{2*7}=\frac{4}{14}
=2/7
$