5n^2-7n=3n^2+5n

Solution for 5n^2-7n=3n^2+5n equation:

5n^2-7n=3n^2+5n

We move all terms to the left:

5n^2-7n-(3n^2+5n)=0

We get rid of parentheses

5n^2-3n^2-7n-5n=0

We add all the numbers together, and all the variables

2n^2-12n=0

a = 2; b = -12; c = 0;
Δ = b2-4ac
Δ = -122-4·2·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-12}{2*2}=\frac{0}{4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+12}{2*2}=\frac{24}{4}
=6
$