3/8n+5(n-6)=1.875n-2

Solution for 3/8n+5(n-6)=1.875n-2 equation:

3/8n+5(n-6)=1.875n-2

We move all terms to the left:

3/8n+5(n-6)-(1.875n-2)=0


Domain of the equation: 8n!=0

n!=0/8

n!=0

n∈R


We multiply parentheses

3/8n+5n-(1.875n-2)-30=0

We get rid of parentheses

3/8n+5n-1.875n+2-30=0

We multiply all the terms by the denominator


5n*8n-(1.875n)*8n+2*8n-30*8n+3=0

We add all the numbers together, and all the variables

5n*8n-(+1.875n)*8n+2*8n-30*8n+3=0

We multiply parentheses

-8n^2+5n*8n+2*8n-30*8n+3=0

Wy multiply elements

-8n^2+40n^2+16n-240n+3=0

We add all the numbers together, and all the variables

32n^2-224n+3=0

a = 32; b = -224; c = +3;
Δ = b2-4ac
Δ = -2242-4·32·3
Δ = 49792
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:

$\sqrt{\Delta}=\sqrt{49792}=\sqrt{64*778}=\sqrt{64}*\sqrt{778}=8\sqrt{778}$
$n_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-224)-8\sqrt{778}}{2*32}=\frac{224-8\sqrt{778}}{64}
$
$n_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-224)+8\sqrt{778}}{2*32}=\frac{224+8\sqrt{778}}{64}
$