20q^2-13q-21=0

Solution for 20q^2-13q-21=0 equation:

20q^2-13q-21=0

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

$\sqrt{\Delta}=\sqrt{1849}=43$
$q_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-43}{2*20}=\frac{-30}{40}
=-3/4
$
$q_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+43}{2*20}=\frac{56}{40}
=1+2/5
$