4-x/2x-1+5=4/3x

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

4-x/2x-1+5=4/3x

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-3x^2)/6x^2+(-8x)/6x^2+8=0

We multiply all the terms by the denominator


(-3x^2)+(-8x)+8*6x^2=0

Wy multiply elements

(-3x^2)+48x^2+(-8x)=0

We get rid of parentheses

-3x^2+48x^2-8x=0

We add all the numbers together, and all the variables

45x^2-8x=0

a = 45; b = -8; c = 0;
Δ = b2-4ac
Δ = -82-4·45·0
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-8}{2*45}=\frac{0}{90}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+8}{2*45}=\frac{16}{90}
=8/45
$