2(n^2+n)=5n

Solution for 2(n^2+n)=5n equation:

2(n^2+n)=5n

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

2n^2-3n=0

a = 2; b = -3; c = 0;
Δ = b2-4ac
Δ = -32-4·2·0
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{-(-3)-3}{2*2}=\frac{0}{4}
=0
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3}{2*2}=\frac{6}{4}
=1+1/2
$