1/2x+4(x-1)=23

Solution for 1/2x+4(x-1)=23 equation:

1/2x+4(x-1)=23

We move all terms to the left:

1/2x+4(x-1)-(23)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

1/2x+4x-4-23=0

We multiply all the terms by the denominator


4x*2x-4*2x-23*2x+1=0

Wy multiply elements

8x^2-8x-46x+1=0

We add all the numbers together, and all the variables

8x^2-54x+1=0

a = 8; b = -54; c = +1;
Δ = b2-4ac
Δ = -542-4·8·1
Δ = 2884
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:

$\sqrt{\Delta}=\sqrt{2884}=\sqrt{4*721}=\sqrt{4}*\sqrt{721}=2\sqrt{721}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{721}}{2*8}=\frac{54-2\sqrt{721}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{721}}{2*8}=\frac{54+2\sqrt{721}}{16}
$