10n(n+7)=2(35+5n)

Solution for 10n(n+7)=2(35+5n) equation:

10n(n+7)=2(35+5n)

We move all terms to the left:

10n(n+7)-(2(35+5n))=0

We add all the numbers together, and all the variables

10n(n+7)-(2(5n+35))=0

We multiply parentheses

10n^2+70n-(2(5n+35))=0


We calculate terms in parentheses: -(2(5n+35)), so:

2(5n+35)

We multiply parentheses

10n+70

Back to the equation:

-(10n+70)


We get rid of parentheses

10n^2+70n-10n-70=0

We add all the numbers together, and all the variables

10n^2+60n-70=0

a = 10; b = 60; c = -70;
Δ = b2-4ac
Δ = 602-4·10·(-70)
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-80}{2*10}=\frac{-140}{20}
=-7
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+80}{2*10}=\frac{20}{20}
=1
$