1/2x-2=28-4x

Solution for 1/2x-2=28-4x equation:

1/2x-2=28-4x

We move all terms to the left:

1/2x-2-(28-4x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-4x+28)-2=0

We get rid of parentheses

1/2x+4x-28-2=0

We multiply all the terms by the denominator


4x*2x-28*2x-2*2x+1=0

Wy multiply elements

8x^2-56x-4x+1=0

We add all the numbers together, and all the variables

8x^2-60x+1=0

a = 8; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·8·1
Δ = 3568
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:

$\sqrt{\Delta}=\sqrt{3568}=\sqrt{16*223}=\sqrt{16}*\sqrt{223}=4\sqrt{223}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{223}}{2*8}=\frac{60-4\sqrt{223}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{223}}{2*8}=\frac{60+4\sqrt{223}}{16}
$