4r^2-9-9=0

Solution for 4r^2-9-9=0 equation:

4r^2-9-9=0

We add all the numbers together, and all the variables

4r^2-18=0

a = 4; b = 0; c = -18;
Δ = b2-4ac
Δ = 02-4·4·(-18)
Δ = 288
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:

$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*4}=\frac{0-12\sqrt{2}}{8}
=-\frac{12\sqrt{2}}{8}
=-\frac{3\sqrt{2}}{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*4}=\frac{0+12\sqrt{2}}{8}
=\frac{12\sqrt{2}}{8}
=\frac{3\sqrt{2}}{2}
$