X+5/2x=21

Solution for X+5/2x=21 equation:

X+5/2X=21

We move all terms to the left:

X+5/2X-(21)=0


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-21*2X+5=0

Wy multiply elements

2X^2-42X+5=0

a = 2; b = -42; c = +5;
Δ = b2-4ac
Δ = -422-4·2·5
Δ = 1724
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:

$\sqrt{\Delta}=\sqrt{1724}=\sqrt{4*431}=\sqrt{4}*\sqrt{431}=2\sqrt{431}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-2\sqrt{431}}{2*2}=\frac{42-2\sqrt{431}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+2\sqrt{431}}{2*2}=\frac{42+2\sqrt{431}}{4}
$