7/x-5=2x

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

7/x-5=2x

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+7/x-5=0

We multiply all the terms by the denominator


-2x*x-5*x+7=0

We add all the numbers together, and all the variables

-5x-2x*x+7=0

Wy multiply elements

-2x^2-5x+7=0

a = -2; b = -5; c = +7;
Δ = b2-4ac
Δ = -52-4·(-2)·7
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-9}{2*-2}=\frac{-4}{-4}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+9}{2*-2}=\frac{14}{-4}
=-3+1/2
$