4x^2+128x-224=0

Solution for 4x^2+128x-224=0 equation:

4x^2+128x-224=0

a = 4; b = 128; c = -224;
Δ = b2-4ac
Δ = 1282-4·4·(-224)
Δ = 19968
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:

$\sqrt{\Delta}=\sqrt{19968}=\sqrt{256*78}=\sqrt{256}*\sqrt{78}=16\sqrt{78}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(128)-16\sqrt{78}}{2*4}=\frac{-128-16\sqrt{78}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(128)+16\sqrt{78}}{2*4}=\frac{-128+16\sqrt{78}}{8}
$