4-6/x^2=-17

Solution for 4-6/x^2=-17 equation:

4-6/x^2=-17

We move all terms to the left:

4-6/x^2-(-17)=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

-6/x^2+21=0

We multiply all the terms by the denominator


21*x^2-6=0

We add all the numbers together, and all the variables

21x^2-6=0

a = 21; b = 0; c = -6;
Δ = b2-4ac
Δ = 02-4·21·(-6)
Δ = 504
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:

$\sqrt{\Delta}=\sqrt{504}=\sqrt{36*14}=\sqrt{36}*\sqrt{14}=6\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{14}}{2*21}=\frac{0-6\sqrt{14}}{42}
=-\frac{6\sqrt{14}}{42}
=-\frac{\sqrt{14}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{14}}{2*21}=\frac{0+6\sqrt{14}}{42}
=\frac{6\sqrt{14}}{42}
=\frac{\sqrt{14}}{7}
$