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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


56x/24x^2+9x/24x^2+(-21x)/24x^2+5=0

We multiply all the terms by the denominator


56x+9x+(-21x)+5*24x^2=0

We add all the numbers together, and all the variables

65x+(-21x)+5*24x^2=0

Wy multiply elements

120x^2+65x+(-21x)=0

We get rid of parentheses

120x^2+65x-21x=0

We add all the numbers together, and all the variables

120x^2+44x=0

a = 120; b = 44; c = 0;
Δ = b2-4ac
Δ = 442-4·120·0
Δ = 1936
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1936}=44$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-44}{2*120}=\frac{-88}{240}
=-11/30
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+44}{2*120}=\frac{0}{240}
=0
$