2400/x=300+6x

Solution for 2400/x=300+6x equation:

2400/x=300+6x

We move all terms to the left:

2400/x-(300+6x)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

2400/x-(6x+300)=0

We get rid of parentheses

2400/x-6x-300=0

We multiply all the terms by the denominator


-6x*x-300*x+2400=0

We add all the numbers together, and all the variables

-300x-6x*x+2400=0

Wy multiply elements

-6x^2-300x+2400=0

a = -6; b = -300; c = +2400;
Δ = b2-4ac
Δ = -3002-4·(-6)·2400
Δ = 147600
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:

$\sqrt{\Delta}=\sqrt{147600}=\sqrt{3600*41}=\sqrt{3600}*\sqrt{41}=60\sqrt{41}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-300)-60\sqrt{41}}{2*-6}=\frac{300-60\sqrt{41}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-300)+60\sqrt{41}}{2*-6}=\frac{300+60\sqrt{41}}{-12}
$