6n^2=8n+22

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

6n^2=8n+22

We move all terms to the left:

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

We get rid of parentheses

6n^2-8n-22=0

a = 6; b = -8; c = -22;
Δ = b2-4ac
Δ = -82-4·6·(-22)
Δ = 592
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:

$\sqrt{\Delta}=\sqrt{592}=\sqrt{16*37}=\sqrt{16}*\sqrt{37}=4\sqrt{37}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-4\sqrt{37}}{2*6}=\frac{8-4\sqrt{37}}{12}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+4\sqrt{37}}{2*6}=\frac{8+4\sqrt{37}}{12}
$