x*x-40*x-224=0

Solution for x*x-40*x-224=0 equation:

x*x-40x-224=0

We add all the numbers together, and all the variables

-40x+x*x-224=0

Wy multiply elements

x^2-40x-224=0

a = 1; b = -40; c = -224;
Δ = b2-4ac
Δ = -402-4·1·(-224)
Δ = 2496
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:

$\sqrt{\Delta}=\sqrt{2496}=\sqrt{64*39}=\sqrt{64}*\sqrt{39}=8\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-40)-8\sqrt{39}}{2*1}=\frac{40-8\sqrt{39}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-40)+8\sqrt{39}}{2*1}=\frac{40+8\sqrt{39}}{2}
$