6a^2-5a-21=0

Solution for 6a^2-5a-21=0 equation:

6a^2-5a-21=0

a = 6; b = -5; c = -21;
Δ = b2-4ac
Δ = -52-4·6·(-21)
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-23}{2*6}=\frac{-18}{12}
=-1+1/2
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+23}{2*6}=\frac{28}{12}
=2+1/3
$