112=121/x2

Solution for 112=121/x2 equation:

112=121/x2

We move all terms to the left:

112-(121/x2)=0


Domain of the equation: x2)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+121/x2)+112=0

We get rid of parentheses

-121/x2+112=0

We multiply all the terms by the denominator


112*x2-121=0

We add all the numbers together, and all the variables

112x^2-121=0

a = 112; b = 0; c = -121;
Δ = b2-4ac
Δ = 02-4·112·(-121)
Δ = 54208
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:

$\sqrt{\Delta}=\sqrt{54208}=\sqrt{7744*7}=\sqrt{7744}*\sqrt{7}=88\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-88\sqrt{7}}{2*112}=\frac{0-88\sqrt{7}}{224}
=-\frac{88\sqrt{7}}{224}
=-\frac{11\sqrt{7}}{28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+88\sqrt{7}}{2*112}=\frac{0+88\sqrt{7}}{224}
=\frac{88\sqrt{7}}{224}
=\frac{11\sqrt{7}}{28}
$