97.35+x=1/4x

Solution for 97.35+x=1/4x equation:

97.35+x=1/4x

We move all terms to the left:

97.35+x-(1/4x)=0


Domain of the equation: 4x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+1/4x)+97.35=0

We get rid of parentheses

x-1/4x+97.35=0

We multiply all the terms by the denominator


x*4x+(97.35)*4x-1=0

We multiply parentheses

x*4x+389.4x-1=0

Wy multiply elements

4x^2+389.4x-1=0

a = 4; b = 389.4; c = -1;
Δ = b2-4ac
Δ = 389.42-4·4·(-1)
Δ = 151648.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(389.4)-\sqrt{151648.36}}{2*4}=\frac{-389.4-\sqrt{151648.36}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(389.4)+\sqrt{151648.36}}{2*4}=\frac{-389.4+\sqrt{151648.36}}{8}
$