21r^2-53r-8=0

Solution for 21r^2-53r-8=0 equation:

21r^2-53r-8=0

a = 21; b = -53; c = -8;
Δ = b2-4ac
Δ = -532-4·21·(-8)
Δ = 3481
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3481}=59$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-53)-59}{2*21}=\frac{-6}{42}
=-1/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-53)+59}{2*21}=\frac{112}{42}
=2+2/3
$