150/x-2x=20

Solution for 150/x-2x=20 equation:

150/x-2x=20

We move all terms to the left:

150/x-2x-(20)=0


Domain of the equation: x!=0

x∈R


We add all the numbers together, and all the variables

-2x+150/x-20=0

We multiply all the terms by the denominator


-2x*x-20*x+150=0

We add all the numbers together, and all the variables

-20x-2x*x+150=0

Wy multiply elements

-2x^2-20x+150=0

a = -2; b = -20; c = +150;
Δ = b2-4ac
Δ = -202-4·(-2)·150
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-40}{2*-2}=\frac{-20}{-4}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+40}{2*-2}=\frac{60}{-4}
=-15
$