5r2-8=39r

Solution for 5r2-8=39r equation:

5r^2-8=39r

We move all terms to the left:

5r^2-8-(39r)=0

a = 5; b = -39; c = -8;
Δ = b2-4ac
Δ = -392-4·5·(-8)
Δ = 1681
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1681}=41$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-39)-41}{2*5}=\frac{-2}{10}
=-1/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-39)+41}{2*5}=\frac{80}{10}
=8
$