-13n-53=-2n(2n-14)

Solution for -13n-53=-2n(2n-14) equation:

-13n-53=-2n(2n-14)

We move all terms to the left:

-13n-53-(-2n(2n-14))=0


We calculate terms in parentheses: -(-2n(2n-14)), so:

-2n(2n-14)

We multiply parentheses

-4n^2+28n

Back to the equation:

-(-4n^2+28n)


We get rid of parentheses

4n^2-28n-13n-53=0

We add all the numbers together, and all the variables

4n^2-41n-53=0

a = 4; b = -41; c = -53;
Δ = b2-4ac
Δ = -412-4·4·(-53)
Δ = 2529
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:

$\sqrt{\Delta}=\sqrt{2529}=\sqrt{9*281}=\sqrt{9}*\sqrt{281}=3\sqrt{281}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-3\sqrt{281}}{2*4}=\frac{41-3\sqrt{281}}{8}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+3\sqrt{281}}{2*4}=\frac{41+3\sqrt{281}}{8}
$