20n*(n+25)=10n*(3n+37)

Solution for 20n*(n+25)=10n*(3n+37) equation:

20n(n+25)=10n(3n+37)

We move all terms to the left:

20n(n+25)-(10n(3n+37))=0

We multiply parentheses

20n^2+500n-(10n(3n+37))=0


We calculate terms in parentheses: -(10n(3n+37)), so:

10n(3n+37)

We multiply parentheses

30n^2+370n

Back to the equation:

-(30n^2+370n)


We get rid of parentheses

20n^2-30n^2+500n-370n=0

We add all the numbers together, and all the variables

-10n^2+130n=0

a = -10; b = 130; c = 0;
Δ = b2-4ac
Δ = 1302-4·(-10)·0
Δ = 16900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16900}=130$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(130)-130}{2*-10}=\frac{-260}{-20}
=+13
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(130)+130}{2*-10}=\frac{0}{-20}
=0
$