5x-5/x=25

Solution for 5x-5/x=25 equation:

5x-5/x=25

We move all terms to the left:

5x-5/x-(25)=0


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


5x*x-25*x-5=0

We add all the numbers together, and all the variables

-25x+5x*x-5=0

Wy multiply elements

5x^2-25x-5=0

a = 5; b = -25; c = -5;
Δ = b2-4ac
Δ = -252-4·5·(-5)
Δ = 725
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:

$\sqrt{\Delta}=\sqrt{725}=\sqrt{25*29}=\sqrt{25}*\sqrt{29}=5\sqrt{29}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-25)-5\sqrt{29}}{2*5}=\frac{25-5\sqrt{29}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-25)+5\sqrt{29}}{2*5}=\frac{25+5\sqrt{29}}{10}
$