9r2-18-r2-5=0

Solution for 9r2-18-r2-5=0 equation:

9r^2-18-r2-5=0

We add all the numbers together, and all the variables

8r^2-23=0

a = 8; b = 0; c = -23;
Δ = b2-4ac
Δ = 02-4·8·(-23)
Δ = 736
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:

$\sqrt{\Delta}=\sqrt{736}=\sqrt{16*46}=\sqrt{16}*\sqrt{46}=4\sqrt{46}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{46}}{2*8}=\frac{0-4\sqrt{46}}{16}
=-\frac{4\sqrt{46}}{16}
=-\frac{\sqrt{46}}{4}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{46}}{2*8}=\frac{0+4\sqrt{46}}{16}
=\frac{4\sqrt{46}}{16}
=\frac{\sqrt{46}}{4}
$