5x-25/x=5

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

5x-25/x=5

We move all terms to the left:

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


Domain of the equation: x!=0

x∈R


We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

5x^2-5x-25=0

a = 5; b = -5; c = -25;
Δ = b2-4ac
Δ = -52-4·5·(-25)
Δ = 525
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:

$\sqrt{\Delta}=\sqrt{525}=\sqrt{25*21}=\sqrt{25}*\sqrt{21}=5\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5\sqrt{21}}{2*5}=\frac{5-5\sqrt{21}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5\sqrt{21}}{2*5}=\frac{5+5\sqrt{21}}{10}
$