2n^2=5n-2

Solution for 2n^2=5n-2 equation:

2n^2=5n-2

We move all terms to the left:

2n^2-(5n-2)=0

We get rid of parentheses

2n^2-5n+2=0

a = 2; b = -5; c = +2;
Δ = b2-4ac
Δ = -52-4·2·2
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-3}{2*2}=\frac{2}{4}
=1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+3}{2*2}=\frac{8}{4}
=2
$