(3)/2x+4=(4)/3x+7

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

(3)/2x+4=(4)/3x+7

We move all terms to the left:

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

We calculate fractions


9x/6x^2+(-8x)/6x^2-7+4=0

We add all the numbers together, and all the variables

9x/6x^2+(-8x)/6x^2-3=0

We multiply all the terms by the denominator


9x+(-8x)-3*6x^2=0

Wy multiply elements

-18x^2+9x+(-8x)=0

We get rid of parentheses

-18x^2+9x-8x=0

We add all the numbers together, and all the variables

-18x^2+x=0

a = -18; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-18)·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*-18}=\frac{-2}{-36}
=1/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-18}=\frac{0}{-36}
=0
$