x=112/52x

Solution for x=112/52x equation:

x=112/52x

We move all terms to the left:

x-(112/52x)=0


Domain of the equation: 52x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(+112/52x)=0

We get rid of parentheses

x-112/52x=0

We multiply all the terms by the denominator


x*52x-112=0

Wy multiply elements

52x^2-112=0

a = 52; b = 0; c = -112;
Δ = b2-4ac
Δ = 02-4·52·(-112)
Δ = 23296
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:

$\sqrt{\Delta}=\sqrt{23296}=\sqrt{256*91}=\sqrt{256}*\sqrt{91}=16\sqrt{91}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{91}}{2*52}=\frac{0-16\sqrt{91}}{104}
=-\frac{16\sqrt{91}}{104}
=-\frac{2\sqrt{91}}{13}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{91}}{2*52}=\frac{0+16\sqrt{91}}{104}
=\frac{16\sqrt{91}}{104}
=\frac{2\sqrt{91}}{13}
$