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)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5x+1/2x-38=0

We multiply all the terms by the denominator


5x*2x-38*2x+1=0

Wy multiply elements

10x^2-76x+1=0

a = 10; b = -76; c = +1;
Δ = b2-4ac
Δ = -762-4·10·1
Δ = 5736
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:

$\sqrt{\Delta}=\sqrt{5736}=\sqrt{4*1434}=\sqrt{4}*\sqrt{1434}=2\sqrt{1434}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-76)-2\sqrt{1434}}{2*10}=\frac{76-2\sqrt{1434}}{20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-76)+2\sqrt{1434}}{2*10}=\frac{76+2\sqrt{1434}}{20}
$