-16x^2+176x=228

Solution for -16x^2+176x=228 equation:

-16x^2+176x=228

We move all terms to the left:

-16x^2+176x-(228)=0

a = -16; b = 176; c = -228;
Δ = b2-4ac
Δ = 1762-4·(-16)·(-228)
Δ = 16384
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16384}=128$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(176)-128}{2*-16}=\frac{-304}{-32}
=9+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(176)+128}{2*-16}=\frac{-48}{-32}
=1+1/2
$