150-x-2x=120/2x

Solution for 150-x-2x=120/2x equation:

150-x-2x=120/2x

We move all terms to the left:

150-x-2x-(120/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-x-2x-(+120/2x)+150=0

We add all the numbers together, and all the variables

-3x-(+120/2x)+150=0

We get rid of parentheses

-3x-120/2x+150=0

We multiply all the terms by the denominator


-3x*2x+150*2x-120=0

Wy multiply elements

-6x^2+300x-120=0

a = -6; b = 300; c = -120;
Δ = b2-4ac
Δ = 3002-4·(-6)·(-120)
Δ = 87120
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:

$\sqrt{\Delta}=\sqrt{87120}=\sqrt{17424*5}=\sqrt{17424}*\sqrt{5}=132\sqrt{5}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-132\sqrt{5}}{2*-6}=\frac{-300-132\sqrt{5}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+132\sqrt{5}}{2*-6}=\frac{-300+132\sqrt{5}}{-12}
$