2n^2-6n+12=10

Solution for 2n^2-6n+12=10 equation:

2n^2-6n+12=10

We move all terms to the left:

2n^2-6n+12-(10)=0

We add all the numbers together, and all the variables

2n^2-6n+2=0

a = 2; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·2·2
Δ = 20
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:

$\sqrt{\Delta}=\sqrt{20}=\sqrt{4*5}=\sqrt{4}*\sqrt{5}=2\sqrt{5}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{5}}{2*2}=\frac{6-2\sqrt{5}}{4}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{5}}{2*2}=\frac{6+2\sqrt{5}}{4}
$