0.2(3n+4)5n=2.2(4-2n)-3.4

Solution for 0.2(3n+4)5n=2.2(4-2n)-3.4 equation:

0.2(3n+4)5n=2.2(4-2n)-3.4

We move all terms to the left:

0.2(3n+4)5n-(2.2(4-2n)-3.4)=0

We add all the numbers together, and all the variables

0.2(3n+4)5n-(2.2(-2n+4)-3.4)=0

We multiply parentheses

3n^2+4n-(2.2(-2n+4)-3.4)=0


We calculate terms in parentheses: -(2.2(-2n+4)-3.4), so:

2.2(-2n+4)-3.4

We multiply parentheses

-4.4n+8.8-3.4

We add all the numbers together, and all the variables

-4.4n+5.4

Back to the equation:

-(-4.4n+5.4)


We get rid of parentheses

3n^2+4n+4.4n-5.4=0

We add all the numbers together, and all the variables

3n^2+8.4n-5.4=0

a = 3; b = 8.4; c = -5.4;
Δ = b2-4ac
Δ = 8.42-4·3·(-5.4)
Δ = 135.36
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{-(8.4)-\sqrt{135.36}}{2*3}=\frac{-8.4-\sqrt{135.36}}{6}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8.4)+\sqrt{135.36}}{2*3}=\frac{-8.4+\sqrt{135.36}}{6}
$