X+1/2x-33=180

Solution for X+1/2x-33=180 equation:

X+1/2X-33=180

We move all terms to the left:

X+1/2X-33-(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-213=0

We multiply all the terms by the denominator


X*2X-213*2X+1=0

Wy multiply elements

2X^2-426X+1=0

a = 2; b = -426; c = +1;
Δ = b2-4ac
Δ = -4262-4·2·1
Δ = 181468
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:

$\sqrt{\Delta}=\sqrt{181468}=\sqrt{4*45367}=\sqrt{4}*\sqrt{45367}=2\sqrt{45367}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-426)-2\sqrt{45367}}{2*2}=\frac{426-2\sqrt{45367}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-426)+2\sqrt{45367}}{2*2}=\frac{426+2\sqrt{45367}}{4}
$