2x-7=10/x

Solution for 2x-7=10/x equation:

2x-7=10/x

We move all terms to the left:

2x-7-(10/x)=0


Domain of the equation: x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

2x-10/x-7=0

We multiply all the terms by the denominator


2x*x-7*x-10=0

We add all the numbers together, and all the variables

-7x+2x*x-10=0

Wy multiply elements

2x^2-7x-10=0

a = 2; b = -7; c = -10;
Δ = b2-4ac
Δ = -72-4·2·(-10)
Δ = 129
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{-(-7)-\sqrt{129}}{2*2}=\frac{7-\sqrt{129}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{129}}{2*2}=\frac{7+\sqrt{129}}{4}
$