48=5r^2+3

Solution for 48=5r^2+3 equation:

48=5r^2+3

We move all terms to the left:

48-(5r^2+3)=0

We get rid of parentheses

-5r^2-3+48=0

We add all the numbers together, and all the variables

-5r^2+45=0

a = -5; b = 0; c = +45;
Δ = b2-4ac
Δ = 02-4·(-5)·45
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-30}{2*-5}=\frac{-30}{-10}
=+3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+30}{2*-5}=\frac{30}{-10}
=-3
$