(-9x^2+2)/(x^2)=0

Solution for (-9x^2+2)/(x^2)=0 equation:

(-9x^2+2)/(x^2)=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


(-9x^2+2)=0

We get rid of parentheses

-9x^2+2=0

a = -9; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-9)·2
Δ = 72
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:

$\sqrt{\Delta}=\sqrt{72}=\sqrt{36*2}=\sqrt{36}*\sqrt{2}=6\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{2}}{2*-9}=\frac{0-6\sqrt{2}}{-18}
=-\frac{6\sqrt{2}}{-18}
=-\frac{\sqrt{2}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{2}}{2*-9}=\frac{0+6\sqrt{2}}{-18}
=\frac{6\sqrt{2}}{-18}
=\frac{\sqrt{2}}{-3}
$