5x-3=125/x

Solution for 5x-3=125/x equation:

5x-3=125/x

We move all terms to the left:

5x-3-(125/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-(+125/x)-3=0

We get rid of parentheses

5x-125/x-3=0

We multiply all the terms by the denominator


5x*x-3*x-125=0

We add all the numbers together, and all the variables

-3x+5x*x-125=0

Wy multiply elements

5x^2-3x-125=0

a = 5; b = -3; c = -125;
Δ = b2-4ac
Δ = -32-4·5·(-125)
Δ = 2509
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{2509}}{2*5}=\frac{3-\sqrt{2509}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{2509}}{2*5}=\frac{3+\sqrt{2509}}{10}
$