1/2x+2(x+12)=12

Solution for 1/2x+2(x+12)=12 equation:

1/2x+2(x+12)=12

We move all terms to the left:

1/2x+2(x+12)-(12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply parentheses

1/2x+2x+24-12=0

We multiply all the terms by the denominator


2x*2x+24*2x-12*2x+1=0

Wy multiply elements

4x^2+48x-24x+1=0

We add all the numbers together, and all the variables

4x^2+24x+1=0

a = 4; b = 24; c = +1;
Δ = b2-4ac
Δ = 242-4·4·1
Δ = 560
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:

$\sqrt{\Delta}=\sqrt{560}=\sqrt{16*35}=\sqrt{16}*\sqrt{35}=4\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-4\sqrt{35}}{2*4}=\frac{-24-4\sqrt{35}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+4\sqrt{35}}{2*4}=\frac{-24+4\sqrt{35}}{8}
$