21r^2-13r-28=-8

Solution for 21r^2-13r-28=-8 equation:

21r^2-13r-28=-8

We move all terms to the left:

21r^2-13r-28-(-8)=0

We add all the numbers together, and all the variables

21r^2-13r-20=0

a = 21; b = -13; c = -20;
Δ = b2-4ac
Δ = -132-4·21·(-20)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-43}{2*21}=\frac{-30}{42}
=-5/7
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+43}{2*21}=\frac{56}{42}
=1+1/3
$