5x=60-5x-25/x

Solution for 5x=60-5x-25/x equation:

5x=60-5x-25/x

We move all terms to the left:

5x-(60-5x-25/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

5x-(-5x-25/x+60)=0

We get rid of parentheses

5x+5x+25/x-60=0

We multiply all the terms by the denominator


5x*x+5x*x-60*x+25=0

We add all the numbers together, and all the variables

-60x+5x*x+5x*x+25=0

Wy multiply elements

5x^2+5x^2-60x+25=0

We add all the numbers together, and all the variables

10x^2-60x+25=0

a = 10; b = -60; c = +25;
Δ = b2-4ac
Δ = -602-4·10·25
Δ = 2600
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:

$\sqrt{\Delta}=\sqrt{2600}=\sqrt{100*26}=\sqrt{100}*\sqrt{26}=10\sqrt{26}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-10\sqrt{26}}{2*10}=\frac{60-10\sqrt{26}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+10\sqrt{26}}{2*10}=\frac{60+10\sqrt{26}}{20}
$