15x+590=20x+545/x=

Solution for 15x+590=20x+545/x= equation:

15x+590=20x+545/x=

We move all terms to the left:

15x+590-(20x+545/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

15x-(+20x+545/x)+590=0

We get rid of parentheses

15x-20x-545/x+590=0

We multiply all the terms by the denominator


15x*x-20x*x+590*x-545=0

We add all the numbers together, and all the variables

590x+15x*x-20x*x-545=0

Wy multiply elements

15x^2-20x^2+590x-545=0

We add all the numbers together, and all the variables

-5x^2+590x-545=0

a = -5; b = 590; c = -545;
Δ = b2-4ac
Δ = 5902-4·(-5)·(-545)
Δ = 337200
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:

$\sqrt{\Delta}=\sqrt{337200}=\sqrt{400*843}=\sqrt{400}*\sqrt{843}=20\sqrt{843}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(590)-20\sqrt{843}}{2*-5}=\frac{-590-20\sqrt{843}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(590)+20\sqrt{843}}{2*-5}=\frac{-590+20\sqrt{843}}{-10}
$