180=22/76^2r-2

Solution for 180=22/76^2r-2 equation:

180=22/76^2r-2

We move all terms to the left:

180-(22/76^2r-2)=0


Domain of the equation: 76^2r-2)!=0

r∈R


We get rid of parentheses

-22/76^2r+2+180=0

We multiply all the terms by the denominator


2*76^2r+180*76^2r-22=0

Wy multiply elements

152r^2+13680r^2-22=0

We add all the numbers together, and all the variables

13832r^2-22=0

a = 13832; b = 0; c = -22;
Δ = b2-4ac
Δ = 02-4·13832·(-22)
Δ = 1217216
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:

$\sqrt{\Delta}=\sqrt{1217216}=\sqrt{64*19019}=\sqrt{64}*\sqrt{19019}=8\sqrt{19019}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{19019}}{2*13832}=\frac{0-8\sqrt{19019}}{27664}
=-\frac{8\sqrt{19019}}{27664}
=-\frac{\sqrt{19019}}{3458}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{19019}}{2*13832}=\frac{0+8\sqrt{19019}}{27664}
=\frac{8\sqrt{19019}}{27664}
=\frac{\sqrt{19019}}{3458}
$