2.5/x^2=6

Solution for 2.5/x^2=6 equation:

2.5/x^2=6

We move all terms to the left:

2.5/x^2-(6)=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


-6*x^2+2.5=0

We add all the numbers together, and all the variables

-6x^2+2.5=0

a = -6; b = 0; c = +2.5;
Δ = b2-4ac
Δ = 02-4·(-6)·2.5
Δ = 60
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:

$\sqrt{\Delta}=\sqrt{60}=\sqrt{4*15}=\sqrt{4}*\sqrt{15}=2\sqrt{15}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{15}}{2*-6}=\frac{0-2\sqrt{15}}{-12}
=-\frac{2\sqrt{15}}{-12}
=-\frac{\sqrt{15}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{15}}{2*-6}=\frac{0+2\sqrt{15}}{-12}
=\frac{2\sqrt{15}}{-12}
=\frac{\sqrt{15}}{-6}
$