6n^2-22n+54=-6n+6+5n^2

Solution for 6n^2-22n+54=-6n+6+5n^2 equation:

6n^2-22n+54=-6n+6+5n^2

We move all terms to the left:

6n^2-22n+54-(-6n+6+5n^2)=0

We get rid of parentheses

6n^2-5n^2+6n-22n-6+54=0

We add all the numbers together, and all the variables

n^2-16n+48=0

a = 1; b = -16; c = +48;
Δ = b2-4ac
Δ = -162-4·1·48
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-8}{2*1}=\frac{8}{2}
=4
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+8}{2*1}=\frac{24}{2}
=12
$