6/x+2=7/2x+5

Solution for 6/x+2=7/2x+5 equation:

6/x+2=7/2x+5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



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

x∈R


We get rid of parentheses

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

We calculate fractions


12x/2x^2+(-7x)/2x^2-5+2=0

We add all the numbers together, and all the variables

12x/2x^2+(-7x)/2x^2-3=0

We multiply all the terms by the denominator


12x+(-7x)-3*2x^2=0

Wy multiply elements

-6x^2+12x+(-7x)=0

We get rid of parentheses

-6x^2+12x-7x=0

We add all the numbers together, and all the variables

-6x^2+5x=0

a = -6; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-6)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-6}=\frac{-10}{-12}
=5/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-6}=\frac{0}{-12}
=0
$