2x+1/2x+x+0.8x=27

Solution for 2x+1/2x+x+0.8x=27 equation:

2x+1/2x+x+0.8x=27

We move all terms to the left:

2x+1/2x+x+0.8x-(27)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

3.8x+1/2x-27=0

We multiply all the terms by the denominator


(3.8x)*2x-27*2x+1=0

We add all the numbers together, and all the variables

(+3.8x)*2x-27*2x+1=0

We multiply parentheses

6x^2-27*2x+1=0

Wy multiply elements

6x^2-54x+1=0

a = 6; b = -54; c = +1;
Δ = b2-4ac
Δ = -542-4·6·1
Δ = 2892
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:

$\sqrt{\Delta}=\sqrt{2892}=\sqrt{4*723}=\sqrt{4}*\sqrt{723}=2\sqrt{723}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{723}}{2*6}=\frac{54-2\sqrt{723}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{723}}{2*6}=\frac{54+2\sqrt{723}}{12}
$