3n^2-8=4n+6

Solution for 3n^2-8=4n+6 equation:

3n^2-8=4n+6

We move all terms to the left:

3n^2-8-(4n+6)=0

We get rid of parentheses

3n^2-4n-6-8=0

We add all the numbers together, and all the variables

3n^2-4n-14=0

a = 3; b = -4; c = -14;
Δ = b2-4ac
Δ = -42-4·3·(-14)
Δ = 184
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:

$\sqrt{\Delta}=\sqrt{184}=\sqrt{4*46}=\sqrt{4}*\sqrt{46}=2\sqrt{46}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{46}}{2*3}=\frac{4-2\sqrt{46}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{46}}{2*3}=\frac{4+2\sqrt{46}}{6}
$