150+1/3x=1x

Solution for 150+1/3x=1x equation:

150+1/3x=1x

We move all terms to the left:

150+1/3x-(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+1/3x+150=0

We multiply all the terms by the denominator


-1x*3x+150*3x+1=0

Wy multiply elements

-3x^2+450x+1=0

a = -3; b = 450; c = +1;
Δ = b2-4ac
Δ = 4502-4·(-3)·1
Δ = 202512
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:

$\sqrt{\Delta}=\sqrt{202512}=\sqrt{16*12657}=\sqrt{16}*\sqrt{12657}=4\sqrt{12657}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(450)-4\sqrt{12657}}{2*-3}=\frac{-450-4\sqrt{12657}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(450)+4\sqrt{12657}}{2*-3}=\frac{-450+4\sqrt{12657}}{-6}
$