1/2=-16x^2+16x+480

Solution for 1/2=-16x^2+16x+480 equation:

1/2=-16x^2+16x+480

We move all terms to the left:

1/2-(-16x^2+16x+480)=0

We get rid of parentheses

16x^2-16x-480+1/2=0

We multiply all the terms by the denominator


16x^2*2-16x*2+1-480*2=0

We add all the numbers together, and all the variables

16x^2*2-16x*2-959=0

Wy multiply elements

32x^2-32x-959=0

a = 32; b = -32; c = -959;
Δ = b2-4ac
Δ = -322-4·32·(-959)
Δ = 123776
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:

$\sqrt{\Delta}=\sqrt{123776}=\sqrt{64*1934}=\sqrt{64}*\sqrt{1934}=8\sqrt{1934}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{1934}}{2*32}=\frac{32-8\sqrt{1934}}{64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{1934}}{2*32}=\frac{32+8\sqrt{1934}}{64}
$