5x^2+8x-224=0

Solution for 5x^2+8x-224=0 equation:

5x^2+8x-224=0

a = 5; b = 8; c = -224;
Δ = b2-4ac
Δ = 82-4·5·(-224)
Δ = 4544
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:

$\sqrt{\Delta}=\sqrt{4544}=\sqrt{64*71}=\sqrt{64}*\sqrt{71}=8\sqrt{71}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-8\sqrt{71}}{2*5}=\frac{-8-8\sqrt{71}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+8\sqrt{71}}{2*5}=\frac{-8+8\sqrt{71}}{10}
$