(8k+k^2-6)-(10k+7-2k^2)=0

Solution for (8k+k^2-6)-(10k+7-2k^2)=0 equation:

(8k+k^2-6)-(10k+7-2k^2)=0

We get rid of parentheses

k^2+2k^2+8k-10k-6-7=0

We add all the numbers together, and all the variables

3k^2-2k-13=0

a = 3; b = -2; c = -13;
Δ = b2-4ac
Δ = -22-4·3·(-13)
Δ = 160
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{160}=\sqrt{16*10}=\sqrt{16}*\sqrt{10}=4\sqrt{10}$
$k_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-4\sqrt{10}}{2*3}=\frac{2-4\sqrt{10}}{6}
$
$k_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+4\sqrt{10}}{2*3}=\frac{2+4\sqrt{10}}{6}
$