5/2x=98-x

Solution for 5/2x=98-x equation:

5/2x=98-x

We move all terms to the left:

5/2x-(98-x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

5/2x-(-1x+98)=0

We get rid of parentheses

5/2x+1x-98=0

We multiply all the terms by the denominator


1x*2x-98*2x+5=0

Wy multiply elements

2x^2-196x+5=0

a = 2; b = -196; c = +5;
Δ = b2-4ac
Δ = -1962-4·2·5
Δ = 38376
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:

$\sqrt{\Delta}=\sqrt{38376}=\sqrt{36*1066}=\sqrt{36}*\sqrt{1066}=6\sqrt{1066}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-196)-6\sqrt{1066}}{2*2}=\frac{196-6\sqrt{1066}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-196)+6\sqrt{1066}}{2*2}=\frac{196+6\sqrt{1066}}{4}
$