4(0.5n-3)=n0.25(12-8n)

Solution for 4(0.5n-3)=n0.25(12-8n) equation:

4(0.5n-3)=n0.25(12-8n)

We move all terms to the left:

4(0.5n-3)-(n0.25(12-8n))=0

We add all the numbers together, and all the variables

4(0.5n-3)-(n0.25(-8n+12))=0

We multiply parentheses

0n-(n0.25(-8n+12))-12=0


We calculate terms in parentheses: -(n0.25(-8n+12)), so:

n0.25(-8n+12)

We multiply parentheses

-8n^2+12n

Back to the equation:

-(-8n^2+12n)


We add all the numbers together, and all the variables

-(-8n^2+12n)+n-12=0

We get rid of parentheses

8n^2-12n+n-12=0

We add all the numbers together, and all the variables

8n^2-11n-12=0

a = 8; b = -11; c = -12;
Δ = b2-4ac
Δ = -112-4·8·(-12)
Δ = 505
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{-(-11)-\sqrt{505}}{2*8}=\frac{11-\sqrt{505}}{16}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{505}}{2*8}=\frac{11+\sqrt{505}}{16}
$