X+1/2x=30

Solution for X+1/2x=30 equation:

X+1/2X=30

We move all terms to the left:

X+1/2X-(30)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-30*2X+1=0

Wy multiply elements

2X^2-60X+1=0

a = 2; b = -60; c = +1;
Δ = b2-4ac
Δ = -602-4·2·1
Δ = 3592
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:

$\sqrt{\Delta}=\sqrt{3592}=\sqrt{4*898}=\sqrt{4}*\sqrt{898}=2\sqrt{898}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-2\sqrt{898}}{2*2}=\frac{60-2\sqrt{898}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+2\sqrt{898}}{2*2}=\frac{60+2\sqrt{898}}{4}
$