2/x-5=5x-7

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

2/x-5=5x-7

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

2x-5x*x+2=0

Wy multiply elements

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

a = -5; b = 2; c = +2;
Δ = b2-4ac
Δ = 22-4·(-5)·2
Δ = 44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2\sqrt{11}}{2*-5}=\frac{-2-2\sqrt{11}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2\sqrt{11}}{2*-5}=\frac{-2+2\sqrt{11}}{-10}
$