5r2-8=32

Solution for 5r2-8=32 equation:

5r^2-8=32

We move all terms to the left:

5r^2-8-(32)=0

We add all the numbers together, and all the variables

5r^2-40=0

a = 5; b = 0; c = -40;
Δ = b2-4ac
Δ = 02-4·5·(-40)
Δ = 800
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:

$\sqrt{\Delta}=\sqrt{800}=\sqrt{400*2}=\sqrt{400}*\sqrt{2}=20\sqrt{2}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-20\sqrt{2}}{2*5}=\frac{0-20\sqrt{2}}{10}
=-\frac{20\sqrt{2}}{10}
=-2\sqrt{2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+20\sqrt{2}}{2*5}=\frac{0+20\sqrt{2}}{10}
=\frac{20\sqrt{2}}{10}
=2\sqrt{2}
$