-n(8n+3)=-n(7n+3)-25

Solution for -n(8n+3)=-n(7n+3)-25 equation:

-n(8n+3)=-n(7n+3)-25

We move all terms to the left:

-n(8n+3)-(-n(7n+3)-25)=0

We multiply parentheses

-8n^2-3n-(-n(7n+3)-25)=0


We calculate terms in parentheses: -(-n(7n+3)-25), so:

-n(7n+3)-25

We multiply parentheses

-7n^2-3n-25

Back to the equation:

-(-7n^2-3n-25)


We get rid of parentheses

-8n^2+7n^2+3n-3n+25=0

We add all the numbers together, and all the variables

-1n^2+25=0

a = -1; b = 0; c = +25;
Δ = b2-4ac
Δ = 02-4·(-1)·25
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10}{2*-1}=\frac{-10}{-2}
=+5
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10}{2*-1}=\frac{10}{-2}
=-5
$