80/x^2=8

Solution for 80/x^2=8 equation:

80/x^2=8

We move all terms to the left:

80/x^2-(8)=0


Domain of the equation: x^2!=0

x^2!=0/

x^2!=√0

x!=0

x∈R


We multiply all the terms by the denominator


-8*x^2+80=0

We add all the numbers together, and all the variables

-8x^2+80=0

a = -8; b = 0; c = +80;
Δ = b2-4ac
Δ = 02-4·(-8)·80
Δ = 2560
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:

$\sqrt{\Delta}=\sqrt{2560}=\sqrt{256*10}=\sqrt{256}*\sqrt{10}=16\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{10}}{2*-8}=\frac{0-16\sqrt{10}}{-16}
=-\frac{16\sqrt{10}}{-16}
=-\frac{\sqrt{10}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{10}}{2*-8}=\frac{0+16\sqrt{10}}{-16}
=\frac{16\sqrt{10}}{-16}
=\frac{\sqrt{10}}{-1}
$