X+1/2x=133

Solution for X+1/2x=133 equation:

X+1/2X=133

We move all terms to the left:

X+1/2X-(133)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-133*2X+1=0

Wy multiply elements

2X^2-266X+1=0

a = 2; b = -266; c = +1;
Δ = b2-4ac
Δ = -2662-4·2·1
Δ = 70748
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:

$\sqrt{\Delta}=\sqrt{70748}=\sqrt{4*17687}=\sqrt{4}*\sqrt{17687}=2\sqrt{17687}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-266)-2\sqrt{17687}}{2*2}=\frac{266-2\sqrt{17687}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-266)+2\sqrt{17687}}{2*2}=\frac{266+2\sqrt{17687}}{4}
$