22-5(3-2n)=2n(5n+32)

Solution for 22-5(3-2n)=2n(5n+32) equation:

22-5(3-2n)=2n(5n+32)

We move all terms to the left:

22-5(3-2n)-(2n(5n+32))=0

We add all the numbers together, and all the variables

-5(-2n+3)-(2n(5n+32))+22=0

We multiply parentheses

10n-(2n(5n+32))-15+22=0


We calculate terms in parentheses: -(2n(5n+32)), so:

2n(5n+32)

We multiply parentheses

10n^2+64n

Back to the equation:

-(10n^2+64n)


We add all the numbers together, and all the variables

10n-(10n^2+64n)+7=0

We get rid of parentheses

-10n^2+10n-64n+7=0

We add all the numbers together, and all the variables

-10n^2-54n+7=0

a = -10; b = -54; c = +7;
Δ = b2-4ac
Δ = -542-4·(-10)·7
Δ = 3196
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:

$\sqrt{\Delta}=\sqrt{3196}=\sqrt{4*799}=\sqrt{4}*\sqrt{799}=2\sqrt{799}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{799}}{2*-10}=\frac{54-2\sqrt{799}}{-20}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{799}}{2*-10}=\frac{54+2\sqrt{799}}{-20}
$