-7/3x+3/2=1/2x-7

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

-7/3x+3/2=1/2x-7

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


(-56x)/24x^2+(-3x)/24x^2+9x/24x^2+7=0

We multiply all the terms by the denominator


(-56x)+(-3x)+9x+7*24x^2=0

We add all the numbers together, and all the variables

9x+(-56x)+(-3x)+7*24x^2=0

Wy multiply elements

168x^2+9x+(-56x)+(-3x)=0

We get rid of parentheses

168x^2+9x-56x-3x=0

We add all the numbers together, and all the variables

168x^2-50x=0

a = 168; b = -50; c = 0;
Δ = b2-4ac
Δ = -502-4·168·0
Δ = 2500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2500}=50$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-50}{2*168}=\frac{0}{336}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+50}{2*168}=\frac{100}{336}
=25/84
$