3*x+60=2400/x

Solution for 3*x+60=2400/x equation:

3x+60=2400/x

We move all terms to the left:

3x+60-(2400/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

3x-(+2400/x)+60=0

We get rid of parentheses

3x-2400/x+60=0

We multiply all the terms by the denominator


3x*x+60*x-2400=0

We add all the numbers together, and all the variables

60x+3x*x-2400=0

Wy multiply elements

3x^2+60x-2400=0

a = 3; b = 60; c = -2400;
Δ = b2-4ac
Δ = 602-4·3·(-2400)
Δ = 32400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{32400}=180$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(60)-180}{2*3}=\frac{-240}{6}
=-40
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(60)+180}{2*3}=\frac{120}{6}
=20
$