-5a^2+33a+56=0

Solution for -5a^2+33a+56=0 equation:

-5a^2+33a+56=0

a = -5; b = 33; c = +56;
Δ = b2-4ac
Δ = 332-4·(-5)·56
Δ = 2209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2209}=47$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(33)-47}{2*-5}=\frac{-80}{-10}
=+8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(33)+47}{2*-5}=\frac{14}{-10}
=-1+2/5
$