8(3/4x+2)=8(3/8x-4)

Solution for 8(3/4x+2)=8(3/8x-4) equation:

8(3/4x+2)=8(3/8x-4)

We move all terms to the left:

8(3/4x+2)-(8(3/8x-4))=0


Domain of the equation: 4x+2)!=0

x∈R



Domain of the equation: 8x-4))!=0

x∈R


We multiply parentheses

24x-(8(3/8x-4))+16=0

We multiply all the terms by the denominator


24x*8x+16*8x-4))-(8(3-4))=0

We add all the numbers together, and all the variables

24x*8x+16*8x-4))-(8(-1))=0

We add all the numbers together, and all the variables

24x*8x+16*8x=0

Wy multiply elements

192x^2+128x=0

a = 192; b = 128; c = 0;
Δ = b2-4ac
Δ = 1282-4·192·0
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-128}{2*192}=\frac{-256}{384}
=-2/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+128}{2*192}=\frac{0}{384}
=0
$