3/4x+1/2x+5/6=3/8

Solution for 3/4x+1/2x+5/6=3/8 equation:

3/4x+1/2x+5/6=3/8

We move all terms to the left:

3/4x+1/2x+5/6-(3/8)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3/4x+1/2x+5/6-(+3/8)=0

We get rid of parentheses

3/4x+1/2x+5/6-3/8=0

We calculate fractions


(-288x^2)/2304x^2+640x^2/2304x^2+1728x/2304x^2+1152x/2304x^2=0

We multiply all the terms by the denominator


(-288x^2)+640x^2+1728x+1152x=0

We add all the numbers together, and all the variables

640x^2+(-288x^2)+2880x=0

We get rid of parentheses

640x^2-288x^2+2880x=0

We add all the numbers together, and all the variables

352x^2+2880x=0

a = 352; b = 2880; c = 0;
Δ = b2-4ac
Δ = 28802-4·352·0
Δ = 8294400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8294400}=2880$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2880)-2880}{2*352}=\frac{-5760}{704}
=-8+2/11
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2880)+2880}{2*352}=\frac{0}{704}
=0
$