110-40x2+16=0

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Solution for 110-40x2+16=0 equation:



110-40x^2+16=0
We add all the numbers together, and all the variables
-40x^2+126=0
a = -40; b = 0; c = +126;
Δ = b2-4ac
Δ = 02-4·(-40)·126
Δ = 20160
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:
$\sqrt{\Delta}=\sqrt{20160}=\sqrt{576*35}=\sqrt{576}*\sqrt{35}=24\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-24\sqrt{35}}{2*-40}=\frac{0-24\sqrt{35}}{-80} =-\frac{24\sqrt{35}}{-80} =-\frac{3\sqrt{35}}{-10} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+24\sqrt{35}}{2*-40}=\frac{0+24\sqrt{35}}{-80} =\frac{24\sqrt{35}}{-80} =\frac{3\sqrt{35}}{-10} $

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