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

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

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

We move all terms to the left:

-3/2x-7/2-(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+7-7/2=0

We calculate fractions


(-9x)/24x^2+(-32x)/24x^2+(-21x)/24x^2+7=0

We multiply all the terms by the denominator


(-9x)+(-32x)+(-21x)+7*24x^2=0

Wy multiply elements

168x^2+(-9x)+(-32x)+(-21x)=0

We get rid of parentheses

168x^2-9x-32x-21x=0

We add all the numbers together, and all the variables

168x^2-62x=0

a = 168; b = -62; c = 0;
Δ = b2-4ac
Δ = -622-4·168·0
Δ = 3844
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3844}=62$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-62)-62}{2*168}=\frac{0}{336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-62)+62}{2*168}=\frac{124}{336}
=31/84
$