4r^2+5=281

Solution for 4r^2+5=281 equation:

4r^2+5=281

We move all terms to the left:

4r^2+5-(281)=0

We add all the numbers together, and all the variables

4r^2-276=0

a = 4; b = 0; c = -276;
Δ = b2-4ac
Δ = 02-4·4·(-276)
Δ = 4416
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:

$\sqrt{\Delta}=\sqrt{4416}=\sqrt{64*69}=\sqrt{64}*\sqrt{69}=8\sqrt{69}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{69}}{2*4}=\frac{0-8\sqrt{69}}{8}
=-\frac{8\sqrt{69}}{8}
=-\sqrt{69}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{69}}{2*4}=\frac{0+8\sqrt{69}}{8}
=\frac{8\sqrt{69}}{8}
=\sqrt{69}
$