x+1/2x=96

Solution for x+1/2x=96 equation:

x+1/2x=96

We move all terms to the left:

x+1/2x-(96)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-96*2x+1=0

Wy multiply elements

2x^2-192x+1=0

a = 2; b = -192; c = +1;
Δ = b2-4ac
Δ = -1922-4·2·1
Δ = 36856
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:

$\sqrt{\Delta}=\sqrt{36856}=\sqrt{4*9214}=\sqrt{4}*\sqrt{9214}=2\sqrt{9214}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-2\sqrt{9214}}{2*2}=\frac{192-2\sqrt{9214}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+2\sqrt{9214}}{2*2}=\frac{192+2\sqrt{9214}}{4}
$