2x+23=1/2(8x)

Solution for 2x+23=1/2(8x) equation:

2x+23=1/2(8x)

We move all terms to the left:

2x+23-(1/2(8x))=0


Domain of the equation: 28x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

2x-(+1/28x)+23=0

We get rid of parentheses

2x-1/28x+23=0

We multiply all the terms by the denominator


2x*28x+23*28x-1=0

Wy multiply elements

56x^2+644x-1=0

a = 56; b = 644; c = -1;
Δ = b2-4ac
Δ = 6442-4·56·(-1)
Δ = 414960
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:

$\sqrt{\Delta}=\sqrt{414960}=\sqrt{16*25935}=\sqrt{16}*\sqrt{25935}=4\sqrt{25935}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(644)-4\sqrt{25935}}{2*56}=\frac{-644-4\sqrt{25935}}{112}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(644)+4\sqrt{25935}}{2*56}=\frac{-644+4\sqrt{25935}}{112}
$