4/x^2=7

Solution for 4/x^2=7 equation:

4/x^2=7

We move all terms to the left:

4/x^2-(7)=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


-7*x^2+4=0

We add all the numbers together, and all the variables

-7x^2+4=0

a = -7; b = 0; c = +4;
Δ = b2-4ac
Δ = 02-4·(-7)·4
Δ = 112
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:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*-7}=\frac{0-4\sqrt{7}}{-14}
=-\frac{4\sqrt{7}}{-14}
=-\frac{2\sqrt{7}}{-7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*-7}=\frac{0+4\sqrt{7}}{-14}
=\frac{4\sqrt{7}}{-14}
=\frac{2\sqrt{7}}{-7}
$