4a^2-18a-400=0

Solution for 4a^2-18a-400=0 equation:

4a^2-18a-400=0

a = 4; b = -18; c = -400;
Δ = b2-4ac
Δ = -182-4·4·(-400)
Δ = 6724
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6724}=82$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-82}{2*4}=\frac{-64}{8}
=-8
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+82}{2*4}=\frac{100}{8}
=12+1/2
$