-6e^2+5e+21=0

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

-6e^2+5e+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:
$e_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$e_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

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