3/4x+6=5+3/8x

Solution for 3/4x+6=5+3/8x equation:

3/4x+6=5+3/8x

We move all terms to the left:

3/4x+6-(5+3/8x)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 8x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x-(3/8x+5)+6=0

We get rid of parentheses

3/4x-3/8x-5+6=0

We calculate fractions


24x/32x^2+(-12x)/32x^2-5+6=0

We add all the numbers together, and all the variables

24x/32x^2+(-12x)/32x^2+1=0

We multiply all the terms by the denominator


24x+(-12x)+1*32x^2=0

Wy multiply elements

32x^2+24x+(-12x)=0

We get rid of parentheses

32x^2+24x-12x=0

We add all the numbers together, and all the variables

32x^2+12x=0

a = 32; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·32·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*32}=\frac{-24}{64}
=-3/8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*32}=\frac{0}{64}
=0
$