2700/r^2=7900

Solution for 2700/r^2=7900 equation:

2700/r^2=7900

We move all terms to the left:

2700/r^2-(7900)=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


-7900*r^2+2700=0

We add all the numbers together, and all the variables

-7900r^2+2700=0

a = -7900; b = 0; c = +2700;
Δ = b2-4ac
Δ = 02-4·(-7900)·2700
Δ = 85320000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{85320000}=\sqrt{360000*237}=\sqrt{360000}*\sqrt{237}=600\sqrt{237}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-600\sqrt{237}}{2*-7900}=\frac{0-600\sqrt{237}}{-15800}
=-\frac{600\sqrt{237}}{-15800}
=-\frac{3\sqrt{237}}{-79}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+600\sqrt{237}}{2*-7900}=\frac{0+600\sqrt{237}}{-15800}
=\frac{600\sqrt{237}}{-15800}
=\frac{3\sqrt{237}}{-79}
$