x^2+12x-224=0

Solution for x^2+12x-224=0 equation:

x^2+12x-224=0

a = 1; b = 12; c = -224;
Δ = b2-4ac
Δ = 122-4·1·(-224)
Δ = 1040
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:

$\sqrt{\Delta}=\sqrt{1040}=\sqrt{16*65}=\sqrt{16}*\sqrt{65}=4\sqrt{65}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-4\sqrt{65}}{2*1}=\frac{-12-4\sqrt{65}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+4\sqrt{65}}{2*1}=\frac{-12+4\sqrt{65}}{2}
$