4r^2=432

Solution for 4r^2=432 equation:

4r^2=432

We move all terms to the left:

4r^2-(432)=0

a = 4; b = 0; c = -432;
Δ = b2-4ac
Δ = 02-4·4·(-432)
Δ = 6912
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:

$\sqrt{\Delta}=\sqrt{6912}=\sqrt{2304*3}=\sqrt{2304}*\sqrt{3}=48\sqrt{3}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-48\sqrt{3}}{2*4}=\frac{0-48\sqrt{3}}{8}
=-\frac{48\sqrt{3}}{8}
=-6\sqrt{3}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+48\sqrt{3}}{2*4}=\frac{0+48\sqrt{3}}{8}
=\frac{48\sqrt{3}}{8}
=6\sqrt{3}
$