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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


9x/6x^2+(-8x)/6x^2+7+5=0

We add all the numbers together, and all the variables

9x/6x^2+(-8x)/6x^2+12=0

We multiply all the terms by the denominator


9x+(-8x)+12*6x^2=0

Wy multiply elements

72x^2+9x+(-8x)=0

We get rid of parentheses

72x^2+9x-8x=0

We add all the numbers together, and all the variables

72x^2+x=0

a = 72; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·72·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*72}=\frac{-2}{144}
=-1/72
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*72}=\frac{0}{144}
=0
$