10=(-9900/(x^2))+21

Solution for 10=(-9900/(x^2))+21 equation:

10=(-9900/(x^2))+21

We move all terms to the left:

10-((-9900/(x^2))+21)=0


Domain of the equation: x^2)+21)!=0

x!=0/1

x!=0

x∈R


We multiply all the terms by the denominator


-((-9900+10*x^2)+21)=0


We calculate terms in parentheses: -((-9900+10*x^2)+21), so:

(-9900+10*x^2)+21

We get rid of parentheses

10*x^2-9900+21

We add all the numbers together, and all the variables

10x^2-9879

Back to the equation:

-(10x^2-9879)


We get rid of parentheses

-10x^2+9879=0

a = -10; b = 0; c = +9879;
Δ = b2-4ac
Δ = 02-4·(-10)·9879
Δ = 395160
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:

$\sqrt{\Delta}=\sqrt{395160}=\sqrt{4*98790}=\sqrt{4}*\sqrt{98790}=2\sqrt{98790}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{98790}}{2*-10}=\frac{0-2\sqrt{98790}}{-20}
=-\frac{2\sqrt{98790}}{-20}
=-\frac{\sqrt{98790}}{-10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{98790}}{2*-10}=\frac{0+2\sqrt{98790}}{-20}
=\frac{2\sqrt{98790}}{-20}
=\frac{\sqrt{98790}}{-10}
$