150=1/2x+2x

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

150=1/2x+2x

We move all terms to the left:

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


Domain of the equation: 2x+2x)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

-2x-1/2x+150=0

We multiply all the terms by the denominator


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

Wy multiply elements

-4x^2+300x-1=0

a = -4; b = 300; c = -1;
Δ = b2-4ac
Δ = 3002-4·(-4)·(-1)
Δ = 89984
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:

$\sqrt{\Delta}=\sqrt{89984}=\sqrt{64*1406}=\sqrt{64}*\sqrt{1406}=8\sqrt{1406}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(300)-8\sqrt{1406}}{2*-4}=\frac{-300-8\sqrt{1406}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(300)+8\sqrt{1406}}{2*-4}=\frac{-300+8\sqrt{1406}}{-8}
$