7k^2=-24-29k

Solution for 7k^2=-24-29k equation:

7k^2=-24-29k

We move all terms to the left:

7k^2-(-24-29k)=0

We add all the numbers together, and all the variables

7k^2-(-29k-24)=0

We get rid of parentheses

7k^2+29k+24=0

a = 7; b = 29; c = +24;
Δ = b2-4ac
Δ = 292-4·7·24
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-13}{2*7}=\frac{-42}{14}
=-3
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+13}{2*7}=\frac{-16}{14}
=-1+1/7
$