X+(2x-20)+(2x-12)+(1/2x+6)=106

Solution for X+(2x-20)+(2x-12)+(1/2x+6)=106 equation:

X+(2X-20)+(2X-12)+(1/2X+6)=106

We move all terms to the left:

X+(2X-20)+(2X-12)+(1/2X+6)-(106)=0


Domain of the equation: 2X+6)!=0

X∈R


We get rid of parentheses

X+2X+2X+1/2X-20-12+6-106=0

We multiply all the terms by the denominator


X*2X+2X*2X+2X*2X-20*2X-12*2X+6*2X-106*2X+1=0

Wy multiply elements

2X^2+4X^2+4X^2-40X-24X+12X-212X+1=0

We add all the numbers together, and all the variables

10X^2-264X+1=0

a = 10; b = -264; c = +1;
Δ = b2-4ac
Δ = -2642-4·10·1
Δ = 69656
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:

$\sqrt{\Delta}=\sqrt{69656}=\sqrt{4*17414}=\sqrt{4}*\sqrt{17414}=2\sqrt{17414}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-264)-2\sqrt{17414}}{2*10}=\frac{264-2\sqrt{17414}}{20}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-264)+2\sqrt{17414}}{2*10}=\frac{264+2\sqrt{17414}}{20}
$