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

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

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

We move all terms to the left:

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


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 3x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(3x+5)/6x^2+(-14x)/6x^2-5=0

We multiply all the terms by the denominator


(3x+5)+(-14x)-5*6x^2=0

Wy multiply elements

-30x^2+(3x+5)+(-14x)=0

We get rid of parentheses

-30x^2+3x-14x+5=0

We add all the numbers together, and all the variables

-30x^2-11x+5=0

a = -30; b = -11; c = +5;
Δ = b2-4ac
Δ = -112-4·(-30)·5
Δ = 721
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{-(-11)-\sqrt{721}}{2*-30}=\frac{11-\sqrt{721}}{-60}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+\sqrt{721}}{2*-30}=\frac{11+\sqrt{721}}{-60}
$