150+30x=1/2x

Solution for 150+30x=1/2x equation:

150+30x=1/2x

We move all terms to the left:

150+30x-(1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

30x-(+1/2x)+150=0

We get rid of parentheses

30x-1/2x+150=0

We multiply all the terms by the denominator


30x*2x+150*2x-1=0

Wy multiply elements

60x^2+300x-1=0

a = 60; b = 300; c = -1;
Δ = b2-4ac
Δ = 3002-4·60·(-1)
Δ = 90240
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:

$\sqrt{\Delta}=\sqrt{90240}=\sqrt{64*1410}=\sqrt{64}*\sqrt{1410}=8\sqrt{1410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-8\sqrt{1410}}{2*60}=\frac{-300-8\sqrt{1410}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+8\sqrt{1410}}{2*60}=\frac{-300+8\sqrt{1410}}{120}
$