6/x=5/2x+7

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

6/x=5/2x+7

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R



Domain of the equation: 2x+7)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


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

We multiply all the terms by the denominator


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

Wy multiply elements

-14x^2+12x+(-5x)=0

We get rid of parentheses

-14x^2+12x-5x=0

We add all the numbers together, and all the variables

-14x^2+7x=0

a = -14; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-14)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-14}=\frac{-14}{-28}
=1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-14}=\frac{0}{-28}
=0
$