x+5/2x=42

Solution for x+5/2x=42 equation:

x+5/2x=42

We move all terms to the left:

x+5/2x-(42)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-42*2x+5=0

Wy multiply elements

2x^2-84x+5=0

a = 2; b = -84; c = +5;
Δ = b2-4ac
Δ = -842-4·2·5
Δ = 7016
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:

$\sqrt{\Delta}=\sqrt{7016}=\sqrt{4*1754}=\sqrt{4}*\sqrt{1754}=2\sqrt{1754}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-84)-2\sqrt{1754}}{2*2}=\frac{84-2\sqrt{1754}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-84)+2\sqrt{1754}}{2*2}=\frac{84+2\sqrt{1754}}{4}
$