7n(2n+1)=2(5+4n)

Solution for 7n(2n+1)=2(5+4n) equation:

7n(2n+1)=2(5+4n)

We move all terms to the left:

7n(2n+1)-(2(5+4n))=0

We add all the numbers together, and all the variables

7n(2n+1)-(2(4n+5))=0

We multiply parentheses

14n^2+7n-(2(4n+5))=0


We calculate terms in parentheses: -(2(4n+5)), so:

2(4n+5)

We multiply parentheses

8n+10

Back to the equation:

-(8n+10)


We get rid of parentheses

14n^2+7n-8n-10=0

We add all the numbers together, and all the variables

14n^2-1n-10=0

a = 14; b = -1; c = -10;
Δ = b2-4ac
Δ = -12-4·14·(-10)
Δ = 561
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{561}}{2*14}=\frac{1-\sqrt{561}}{28}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{561}}{2*14}=\frac{1+\sqrt{561}}{28}
$