2n^2=10n-12

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

2n^2=10n-12

We move all terms to the left:

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

We get rid of parentheses

2n^2-10n+12=0

a = 2; b = -10; c = +12;
Δ = b2-4ac
Δ = -102-4·2·12
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{-(-10)-2}{2*2}=\frac{8}{4}
=2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2}{2*2}=\frac{12}{4}
=3
$