X+1/2x=288

Solution for X+1/2x=288 equation:

X+1/2X=288

We move all terms to the left:

X+1/2X-(288)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-288*2X+1=0

Wy multiply elements

2X^2-576X+1=0

a = 2; b = -576; c = +1;
Δ = b2-4ac
Δ = -5762-4·2·1
Δ = 331768
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:

$\sqrt{\Delta}=\sqrt{331768}=\sqrt{4*82942}=\sqrt{4}*\sqrt{82942}=2\sqrt{82942}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-576)-2\sqrt{82942}}{2*2}=\frac{576-2\sqrt{82942}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-576)+2\sqrt{82942}}{2*2}=\frac{576+2\sqrt{82942}}{4}
$