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

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

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

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


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

We multiply all the terms by the denominator


(10x+2)+(-7x)-3*2x^2=0

Wy multiply elements

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

We get rid of parentheses

-6x^2+10x-7x+2=0

We add all the numbers together, and all the variables

-6x^2+3x+2=0

a = -6; b = 3; c = +2;
Δ = b2-4ac
Δ = 32-4·(-6)·2
Δ = 57
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{-(3)-\sqrt{57}}{2*-6}=\frac{-3-\sqrt{57}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*-6}=\frac{-3+\sqrt{57}}{-12}
$