7-2n=8n-(-4n)n=

Solution for 7-2n=8n-(-4n)n= equation:

7-2n=8n-(-4n)n=

We move all terms to the left:

7-2n-(8n-(-4n)n)=0


We calculate terms in parentheses: -(8n-(-4n)n), so:

8n-(-4n)n

We multiply parentheses

4n^2+8n

Back to the equation:

-(4n^2+8n)


We get rid of parentheses

-4n^2-2n-8n+7=0

We add all the numbers together, and all the variables

-4n^2-10n+7=0

a = -4; b = -10; c = +7;
Δ = b2-4ac
Δ = -102-4·(-4)·7
Δ = 212
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{212}=\sqrt{4*53}=\sqrt{4}*\sqrt{53}=2\sqrt{53}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{53}}{2*-4}=\frac{10-2\sqrt{53}}{-8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{53}}{2*-4}=\frac{10+2\sqrt{53}}{-8}
$