43=19953/x^2

Solution for 43=19953/x^2 equation:

43=19953/x^2

We move all terms to the left:

43-(19953/x^2)=0


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

x!=0/1

x!=0

x∈R


We get rid of parentheses

-19953/x^2+43=0

We multiply all the terms by the denominator


43*x^2-19953=0

We add all the numbers together, and all the variables

43x^2-19953=0

a = 43; b = 0; c = -19953;
Δ = b2-4ac
Δ = 02-4·43·(-19953)
Δ = 3431916
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:

$\sqrt{\Delta}=\sqrt{3431916}=\sqrt{36*95331}=\sqrt{36}*\sqrt{95331}=6\sqrt{95331}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{95331}}{2*43}=\frac{0-6\sqrt{95331}}{86}
=-\frac{6\sqrt{95331}}{86}
=-\frac{3\sqrt{95331}}{43}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{95331}}{2*43}=\frac{0+6\sqrt{95331}}{86}
=\frac{6\sqrt{95331}}{86}
=\frac{3\sqrt{95331}}{43}
$