2n^2-4n+5=5-3n^2

Solution for 2n^2-4n+5=5-3n^2 equation:

2n^2-4n+5=5-3n^2

We move all terms to the left:

2n^2-4n+5-(5-3n^2)=0

We get rid of parentheses

2n^2+3n^2-4n-5+5=0

We add all the numbers together, and all the variables

5n^2-4n=0

a = 5; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·5·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*5}=\frac{0}{10}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*5}=\frac{8}{10}
=4/5
$