6n^2=8+22n

Solution for 6n^2=8+22n equation:

6n^2=8+22n

We move all terms to the left:

6n^2-(8+22n)=0

We add all the numbers together, and all the variables

6n^2-(22n+8)=0

We get rid of parentheses

6n^2-22n-8=0

a = 6; b = -22; c = -8;
Δ = b2-4ac
Δ = -222-4·6·(-8)
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-26}{2*6}=\frac{-4}{12}
=-1/3
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+26}{2*6}=\frac{48}{12}
=4
$