9r^2-8=217

Solution for 9r^2-8=217 equation:

9r^2-8=217

We move all terms to the left:

9r^2-8-(217)=0

We add all the numbers together, and all the variables

9r^2-225=0

a = 9; b = 0; c = -225;
Δ = b2-4ac
Δ = 02-4·9·(-225)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90}{2*9}=\frac{-90}{18}
=-5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90}{2*9}=\frac{90}{18}
=5
$