300+2/3x=1x

Solution for 300+2/3x=1x equation:

300+2/3x=1x

We move all terms to the left:

300+2/3x-(1x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+2/3x+300=0

We multiply all the terms by the denominator


-1x*3x+300*3x+2=0

Wy multiply elements

-3x^2+900x+2=0

a = -3; b = 900; c = +2;
Δ = b2-4ac
Δ = 9002-4·(-3)·2
Δ = 810024
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:

$\sqrt{\Delta}=\sqrt{810024}=\sqrt{4*202506}=\sqrt{4}*\sqrt{202506}=2\sqrt{202506}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(900)-2\sqrt{202506}}{2*-3}=\frac{-900-2\sqrt{202506}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(900)+2\sqrt{202506}}{2*-3}=\frac{-900+2\sqrt{202506}}{-6}
$