11a^2-32a-37=0

Solution for 11a^2-32a-37=0 equation:

11a^2-32a-37=0

a = 11; b = -32; c = -37;
Δ = b2-4ac
Δ = -322-4·11·(-37)
Δ = 2652
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2652}=\sqrt{4*663}=\sqrt{4}*\sqrt{663}=2\sqrt{663}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-2\sqrt{663}}{2*11}=\frac{32-2\sqrt{663}}{22}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+2\sqrt{663}}{2*11}=\frac{32+2\sqrt{663}}{22}
$