-16x^2+224x=768

Solution for -16x^2+224x=768 equation:

-16x^2+224x=768

We move all terms to the left:

-16x^2+224x-(768)=0

a = -16; b = 224; c = -768;
Δ = b2-4ac
Δ = 2242-4·(-16)·(-768)
Δ = 1024
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1024}=32$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(224)-32}{2*-16}=\frac{-256}{-32}
=+8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(224)+32}{2*-16}=\frac{-192}{-32}
=+6
$