9r2-25=8

Solution for 9r2-25=8 equation:

9r^2-25=8

We move all terms to the left:

9r^2-25-(8)=0

We add all the numbers together, and all the variables

9r^2-33=0

a = 9; b = 0; c = -33;
Δ = b2-4ac
Δ = 02-4·9·(-33)
Δ = 1188
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:

$\sqrt{\Delta}=\sqrt{1188}=\sqrt{36*33}=\sqrt{36}*\sqrt{33}=6\sqrt{33}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{33}}{2*9}=\frac{0-6\sqrt{33}}{18}
=-\frac{6\sqrt{33}}{18}
=-\frac{\sqrt{33}}{3}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{33}}{2*9}=\frac{0+6\sqrt{33}}{18}
=\frac{6\sqrt{33}}{18}
=\frac{\sqrt{33}}{3}
$