9/x^2-43=76

Solution for 9/x^2-43=76 equation:

9/x^2-43=76

We move all terms to the left:

9/x^2-43-(76)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

9/x^2-119=0

We multiply all the terms by the denominator


-119*x^2+9=0

We add all the numbers together, and all the variables

-119x^2+9=0

a = -119; b = 0; c = +9;
Δ = b2-4ac
Δ = 02-4·(-119)·9
Δ = 4284
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:

$\sqrt{\Delta}=\sqrt{4284}=\sqrt{36*119}=\sqrt{36}*\sqrt{119}=6\sqrt{119}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{119}}{2*-119}=\frac{0-6\sqrt{119}}{-238}
=-\frac{6\sqrt{119}}{-238}
=-\frac{3\sqrt{119}}{-119}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{119}}{2*-119}=\frac{0+6\sqrt{119}}{-238}
=\frac{6\sqrt{119}}{-238}
=\frac{3\sqrt{119}}{-119}
$