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

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

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

We move all terms to the left:

7/2x-7/2-(-5/3x-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

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

We calculate fractions


21x/24x^2+40x/24x^2+(-21x)/24x^2+7=0

We multiply all the terms by the denominator


21x+40x+(-21x)+7*24x^2=0

We add all the numbers together, and all the variables

61x+(-21x)+7*24x^2=0

Wy multiply elements

168x^2+61x+(-21x)=0

We get rid of parentheses

168x^2+61x-21x=0

We add all the numbers together, and all the variables

168x^2+40x=0

a = 168; b = 40; c = 0;
Δ = b2-4ac
Δ = 402-4·168·0
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-40}{2*168}=\frac{-80}{336}
=-5/21
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+40}{2*168}=\frac{0}{336}
=0
$