8n^2=22-2n

Solution for 8n^2=22-2n equation:

8n^2=22-2n

We move all terms to the left:

8n^2-(22-2n)=0

We add all the numbers together, and all the variables

8n^2-(-2n+22)=0

We get rid of parentheses

8n^2+2n-22=0

a = 8; b = 2; c = -22;
Δ = b2-4ac
Δ = 22-4·8·(-22)
Δ = 708
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{708}=\sqrt{4*177}=\sqrt{4}*\sqrt{177}=2\sqrt{177}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{177}}{2*8}=\frac{-2-2\sqrt{177}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{177}}{2*8}=\frac{-2+2\sqrt{177}}{16}
$