X+1/2x=69

Solution for X+1/2x=69 equation:

X+1/2X=69

We move all terms to the left:

X+1/2X-(69)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-69*2X+1=0

Wy multiply elements

2X^2-138X+1=0

a = 2; b = -138; c = +1;
Δ = b2-4ac
Δ = -1382-4·2·1
Δ = 19036
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:

$\sqrt{\Delta}=\sqrt{19036}=\sqrt{4*4759}=\sqrt{4}*\sqrt{4759}=2\sqrt{4759}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-138)-2\sqrt{4759}}{2*2}=\frac{138-2\sqrt{4759}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-138)+2\sqrt{4759}}{2*2}=\frac{138+2\sqrt{4759}}{4}
$