x+5/2x=8

Solution for x+5/2x=8 equation:

x+5/2x=8

We move all terms to the left:

x+5/2x-(8)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-8*2x+5=0

Wy multiply elements

2x^2-16x+5=0

a = 2; b = -16; c = +5;
Δ = b2-4ac
Δ = -162-4·2·5
Δ = 216
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:

$\sqrt{\Delta}=\sqrt{216}=\sqrt{36*6}=\sqrt{36}*\sqrt{6}=6\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-6\sqrt{6}}{2*2}=\frac{16-6\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+6\sqrt{6}}{2*2}=\frac{16+6\sqrt{6}}{4}
$