-16x^2+84x+224=0

Solution for -16x^2+84x+224=0 equation:

-16x^2+84x+224=0

a = -16; b = 84; c = +224;
Δ = b2-4ac
Δ = 842-4·(-16)·224
Δ = 21392
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:

$\sqrt{\Delta}=\sqrt{21392}=\sqrt{16*1337}=\sqrt{16}*\sqrt{1337}=4\sqrt{1337}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(84)-4\sqrt{1337}}{2*-16}=\frac{-84-4\sqrt{1337}}{-32}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(84)+4\sqrt{1337}}{2*-16}=\frac{-84+4\sqrt{1337}}{-32}
$