4n^2-6n=-2

Solution for 4n^2-6n=-2 equation:

4n^2-6n=-2

We move all terms to the left:

4n^2-6n-(-2)=0

We add all the numbers together, and all the variables

4n^2-6n+2=0

a = 4; b = -6; c = +2;
Δ = b2-4ac
Δ = -62-4·4·2
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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