0=-16x2+32x+5

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Solution for 0=-16x2+32x+5 equation:



0=-16x^2+32x+5
We move all terms to the left:
0-(-16x^2+32x+5)=0
We add all the numbers together, and all the variables
-(-16x^2+32x+5)=0
We get rid of parentheses
16x^2-32x-5=0
a = 16; b = -32; c = -5;
Δ = b2-4ac
Δ = -322-4·16·(-5)
Δ = 1344
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:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-8\sqrt{21}}{2*16}=\frac{32-8\sqrt{21}}{32} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+8\sqrt{21}}{2*16}=\frac{32+8\sqrt{21}}{32} $

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