(10/x^2+1)-5=3

Solution for (10/x^2+1)-5=3 equation:

(10/x^2+1)-5=3

We move all terms to the left:

(10/x^2+1)-5-(3)=0


Domain of the equation: x^2+1)!=0

x∈R


We add all the numbers together, and all the variables

(10/x^2+1)-8=0

We get rid of parentheses

10/x^2+1-8=0

We multiply all the terms by the denominator


1*x^2-8*x^2+10=0

We add all the numbers together, and all the variables

-7x^2+10=0

a = -7; b = 0; c = +10;
Δ = b2-4ac
Δ = 02-4·(-7)·10
Δ = 280
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:

$\sqrt{\Delta}=\sqrt{280}=\sqrt{4*70}=\sqrt{4}*\sqrt{70}=2\sqrt{70}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{70}}{2*-7}=\frac{0-2\sqrt{70}}{-14}
=-\frac{2\sqrt{70}}{-14}
=-\frac{\sqrt{70}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{70}}{2*-7}=\frac{0+2\sqrt{70}}{-14}
=\frac{2\sqrt{70}}{-14}
=\frac{\sqrt{70}}{-7}
$