(x^2)-44x-84=0

Solution for (x^2)-44x-84=0 equation:

(x^2)-44x-84=0

a = 1; b = -44; c = -84;
Δ = b2-4ac
Δ = -442-4·1·(-84)
Δ = 2272
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2272}=\sqrt{16*142}=\sqrt{16}*\sqrt{142}=4\sqrt{142}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{142}}{2*1}=\frac{44-4\sqrt{142}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{142}}{2*1}=\frac{44+4\sqrt{142}}{2}
$