9r^2-10=647

Solution for 9r^2-10=647 equation:

9r^2-10=647

We move all terms to the left:

9r^2-10-(647)=0

We add all the numbers together, and all the variables

9r^2-657=0

a = 9; b = 0; c = -657;
Δ = b2-4ac
Δ = 02-4·9·(-657)
Δ = 23652
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:

$\sqrt{\Delta}=\sqrt{23652}=\sqrt{324*73}=\sqrt{324}*\sqrt{73}=18\sqrt{73}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{73}}{2*9}=\frac{0-18\sqrt{73}}{18}
=-\frac{18\sqrt{73}}{18}
=-\sqrt{73}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{73}}{2*9}=\frac{0+18\sqrt{73}}{18}
=\frac{18\sqrt{73}}{18}
=\sqrt{73}
$