2x-150=1/2x+100

Solution for 2x-150=1/2x+100 equation:

2x-150=1/2x+100

We move all terms to the left:

2x-150-(1/2x+100)=0


Domain of the equation: 2x+100)!=0

x∈R


We get rid of parentheses

2x-1/2x-100-150=0

We multiply all the terms by the denominator


2x*2x-100*2x-150*2x-1=0

Wy multiply elements

4x^2-200x-300x-1=0

We add all the numbers together, and all the variables

4x^2-500x-1=0

a = 4; b = -500; c = -1;
Δ = b2-4ac
Δ = -5002-4·4·(-1)
Δ = 250016
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:

$\sqrt{\Delta}=\sqrt{250016}=\sqrt{16*15626}=\sqrt{16}*\sqrt{15626}=4\sqrt{15626}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-500)-4\sqrt{15626}}{2*4}=\frac{500-4\sqrt{15626}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-500)+4\sqrt{15626}}{2*4}=\frac{500+4\sqrt{15626}}{8}
$