7k2-8=-10k

Solution for 7k2-8=-10k equation:

7k^2-8=-10k

We move all terms to the left:

7k^2-8-(-10k)=0

We get rid of parentheses

7k^2+10k-8=0

a = 7; b = 10; c = -8;
Δ = b2-4ac
Δ = 102-4·7·(-8)
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-18}{2*7}=\frac{-28}{14}
=-2
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+18}{2*7}=\frac{8}{14}
=4/7
$