5r^2-8r-1=3

Solution for 5r^2-8r-1=3 equation:

5r^2-8r-1=3

We move all terms to the left:

5r^2-8r-1-(3)=0

We add all the numbers together, and all the variables

5r^2-8r-4=0

a = 5; b = -8; c = -4;
Δ = b2-4ac
Δ = -82-4·5·(-4)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-12}{2*5}=\frac{-4}{10}
=-2/5
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+12}{2*5}=\frac{20}{10}
=2
$