5r^2+8=413

Solution for 5r^2+8=413 equation:

5r^2+8=413

We move all terms to the left:

5r^2+8-(413)=0

We add all the numbers together, and all the variables

5r^2-405=0

a = 5; b = 0; c = -405;
Δ = b2-4ac
Δ = 02-4·5·(-405)
Δ = 8100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{8100}=90$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-90}{2*5}=\frac{-90}{10}
=-9
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+90}{2*5}=\frac{90}{10}
=9
$