4n(n-10)=7(-2n+2)

Solution for 4n(n-10)=7(-2n+2) equation:

4n(n-10)=7(-2n+2)

We move all terms to the left:

4n(n-10)-(7(-2n+2))=0

We multiply parentheses

4n^2-40n-(7(-2n+2))=0


We calculate terms in parentheses: -(7(-2n+2)), so:

7(-2n+2)

We multiply parentheses

-14n+14

Back to the equation:

-(-14n+14)


We get rid of parentheses

4n^2-40n+14n-14=0

We add all the numbers together, and all the variables

4n^2-26n-14=0

a = 4; b = -26; c = -14;
Δ = b2-4ac
Δ = -262-4·4·(-14)
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-30}{2*4}=\frac{-4}{8}
=-1/2
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+30}{2*4}=\frac{56}{8}
=7
$