8r^2-r-1=0

Solution for 8r^2-r-1=0 equation:

8r^2-r-1=0

We add all the numbers together, and all the variables

8r^2-1r-1=0

a = 8; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·8·(-1)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{33}}{2*8}=\frac{1-\sqrt{33}}{16}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{33}}{2*8}=\frac{1+\sqrt{33}}{16}
$