X+1/2x+4*1/2x=168

Solution for X+1/2x+4*1/2x=168 equation:

X+1/2X+4*1/2X=168

We move all terms to the left:

X+1/2X+4*1/2X-(168)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-168*2X+1+4*1=0

We add all the numbers together, and all the variables

X*2X-168*2X+5=0

Wy multiply elements

2X^2-336X+5=0

a = 2; b = -336; c = +5;
Δ = b2-4ac
Δ = -3362-4·2·5
Δ = 112856
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:

$\sqrt{\Delta}=\sqrt{112856}=\sqrt{4*28214}=\sqrt{4}*\sqrt{28214}=2\sqrt{28214}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-336)-2\sqrt{28214}}{2*2}=\frac{336-2\sqrt{28214}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-336)+2\sqrt{28214}}{2*2}=\frac{336+2\sqrt{28214}}{4}
$