X+(1/2x)=177

Solution for X+(1/2x)=177 equation:

X+(1/2X)=177

We move all terms to the left:

X+(1/2X)-(177)=0


Domain of the equation: 2X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

X+(+1/2X)-177=0

We get rid of parentheses

X+1/2X-177=0

We multiply all the terms by the denominator


X*2X-177*2X+1=0

Wy multiply elements

2X^2-354X+1=0

a = 2; b = -354; c = +1;
Δ = b2-4ac
Δ = -3542-4·2·1
Δ = 125308
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:

$\sqrt{\Delta}=\sqrt{125308}=\sqrt{4*31327}=\sqrt{4}*\sqrt{31327}=2\sqrt{31327}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-354)-2\sqrt{31327}}{2*2}=\frac{354-2\sqrt{31327}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-354)+2\sqrt{31327}}{2*2}=\frac{354+2\sqrt{31327}}{4}
$