2r2-r-21=0

Solution for 2r2-r-21=0 equation:

2r^2-r-21=0

We add all the numbers together, and all the variables

2r^2-1r-21=0

a = 2; b = -1; c = -21;
Δ = b2-4ac
Δ = -12-4·2·(-21)
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-13}{2*2}=\frac{-12}{4}
=-3
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+13}{2*2}=\frac{14}{4}
=3+1/2
$