4/3x+5/3=7+1/2x

Solution for 4/3x+5/3=7+1/2x equation:

4/3x+5/3=7+1/2x

We move all terms to the left:

4/3x+5/3-(7+1/2x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4/3x-(1/2x+7)+5/3=0

We get rid of parentheses

4/3x-1/2x-7+5/3=0

We calculate fractions


8x/54x^2+(-27x)/54x^2+10x/54x^2-7=0

We multiply all the terms by the denominator


8x+(-27x)+10x-7*54x^2=0

We add all the numbers together, and all the variables

18x+(-27x)-7*54x^2=0

Wy multiply elements

-378x^2+18x+(-27x)=0

We get rid of parentheses

-378x^2+18x-27x=0

We add all the numbers together, and all the variables

-378x^2-9x=0

a = -378; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-378)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-378}=\frac{0}{-756}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-378}=\frac{18}{-756}
=-1/42
$