X+1/2x+21/2x-1=180

Solution for X+1/2x+21/2x-1=180 equation:

X+1/2X+21/2X-1=180

We move all terms to the left:

X+1/2X+21/2X-1-(180)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We add all the numbers together, and all the variables

X+1/2X+21/2X-181=0

We multiply all the terms by the denominator


X*2X-181*2X+1+21=0

We add all the numbers together, and all the variables

X*2X-181*2X+22=0

Wy multiply elements

2X^2-362X+22=0

a = 2; b = -362; c = +22;
Δ = b2-4ac
Δ = -3622-4·2·22
Δ = 130868
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:

$\sqrt{\Delta}=\sqrt{130868}=\sqrt{4*32717}=\sqrt{4}*\sqrt{32717}=2\sqrt{32717}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-362)-2\sqrt{32717}}{2*2}=\frac{362-2\sqrt{32717}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-362)+2\sqrt{32717}}{2*2}=\frac{362+2\sqrt{32717}}{4}
$