-1/3x+5/2=-7/2x-3

Solution for -1/3x+5/2=-7/2x-3 equation:

-1/3x+5/2=-7/2x-3

We move all terms to the left:

-1/3x+5/2-(-7/2x-3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 2x-3)!=0

x∈R


We get rid of parentheses

-1/3x+7/2x+3+5/2=0

We calculate fractions


(-8x)/24x^2+21x/24x^2+15x/24x^2+3=0

We multiply all the terms by the denominator


(-8x)+21x+15x+3*24x^2=0

We add all the numbers together, and all the variables

36x+(-8x)+3*24x^2=0

Wy multiply elements

72x^2+36x+(-8x)=0

We get rid of parentheses

72x^2+36x-8x=0

We add all the numbers together, and all the variables

72x^2+28x=0

a = 72; b = 28; c = 0;
Δ = b2-4ac
Δ = 282-4·72·0
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(28)-28}{2*72}=\frac{-56}{144}
=-7/18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(28)+28}{2*72}=\frac{0}{144}
=0
$