2x+24=300+1/2X

Solution for 2x+24=300+1/2X equation:

2x+24=300+1/2x

We move all terms to the left:

2x+24-(300+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

2x-(1/2x+300)+24=0

We get rid of parentheses

2x-1/2x-300+24=0

We multiply all the terms by the denominator


2x*2x-300*2x+24*2x-1=0

Wy multiply elements

4x^2-600x+48x-1=0

We add all the numbers together, and all the variables

4x^2-552x-1=0

a = 4; b = -552; c = -1;
Δ = b2-4ac
Δ = -5522-4·4·(-1)
Δ = 304720
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:

$\sqrt{\Delta}=\sqrt{304720}=\sqrt{16*19045}=\sqrt{16}*\sqrt{19045}=4\sqrt{19045}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-552)-4\sqrt{19045}}{2*4}=\frac{552-4\sqrt{19045}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-552)+4\sqrt{19045}}{2*4}=\frac{552+4\sqrt{19045}}{8}
$