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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x+4)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


10x/6x^2+(-21x)/6x^2-4+5=0

We add all the numbers together, and all the variables

10x/6x^2+(-21x)/6x^2+1=0

We multiply all the terms by the denominator


10x+(-21x)+1*6x^2=0

Wy multiply elements

6x^2+10x+(-21x)=0

We get rid of parentheses

6x^2+10x-21x=0

We add all the numbers together, and all the variables

6x^2-11x=0

a = 6; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·6·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*6}=\frac{0}{12}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*6}=\frac{22}{12}
=1+5/6
$