2x/3x+5=3/4+x

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

2x/3x+5=3/4+x

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



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

We move all terms containing x to the left, all other terms to the right

x)!=-4

x!=-4/1

x!=-4

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x/3x-x+5-3/4=0

We calculate fractions


-x+8x/12x+(-9x)/12x+5=0

We add all the numbers together, and all the variables

-1x+8x/12x+(-9x)/12x+5=0

We multiply all the terms by the denominator


-1x*12x+8x+(-9x)+5*12x=0

We add all the numbers together, and all the variables

8x-1x*12x+(-9x)+5*12x=0

Wy multiply elements

-12x^2+8x+(-9x)+60x=0

We get rid of parentheses

-12x^2+8x-9x+60x=0

We add all the numbers together, and all the variables

-12x^2+59x=0

a = -12; b = 59; c = 0;
Δ = b2-4ac
Δ = 592-4·(-12)·0
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(59)-59}{2*-12}=\frac{-118}{-24}
=4+11/12
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(59)+59}{2*-12}=\frac{0}{-24}
=0
$