7/2x-5/2x=20/3x+10

Solution for 7/2x-5/2x=20/3x+10 equation:

7/2x-5/2x=20/3x+10

We move all terms to the left:

7/2x-5/2x-(20/3x+10)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x+10)!=0

x∈R


We get rid of parentheses

7/2x-5/2x-20/3x-10=0

We calculate fractions


(-15x+7)/6x^2+(-40x)/6x^2-10=0

We multiply all the terms by the denominator


(-15x+7)+(-40x)-10*6x^2=0

Wy multiply elements

-60x^2+(-15x+7)+(-40x)=0

We get rid of parentheses

-60x^2-15x-40x+7=0

We add all the numbers together, and all the variables

-60x^2-55x+7=0

a = -60; b = -55; c = +7;
Δ = b2-4ac
Δ = -552-4·(-60)·7
Δ = 4705
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-\sqrt{4705}}{2*-60}=\frac{55-\sqrt{4705}}{-120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+\sqrt{4705}}{2*-60}=\frac{55+\sqrt{4705}}{-120}
$