3/r^2-147=0

Solution for 3/r^2-147=0 equation:

3/r^2-147=0


Domain of the equation: r^2!=0

r^2!=0/

r^2!=√0

r!=0

r∈R


We multiply all the terms by the denominator


-147*r^2+3=0

We add all the numbers together, and all the variables

-147r^2+3=0

a = -147; b = 0; c = +3;
Δ = b2-4ac
Δ = 02-4·(-147)·3
Δ = 1764
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1764}=42$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-42}{2*-147}=\frac{-42}{-294}
=1/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+42}{2*-147}=\frac{42}{-294}
=-1/7
$