x=-16x^2+176x+53

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Solution for x=-16x^2+176x+53 equation:



x=-16x^2+176x+53
We move all terms to the left:
x-(-16x^2+176x+53)=0
We get rid of parentheses
16x^2-176x+x-53=0
We add all the numbers together, and all the variables
16x^2-175x-53=0
a = 16; b = -175; c = -53;
Δ = b2-4ac
Δ = -1752-4·16·(-53)
Δ = 34017
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-175)-\sqrt{34017}}{2*16}=\frac{175-\sqrt{34017}}{32} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-175)+\sqrt{34017}}{2*16}=\frac{175+\sqrt{34017}}{32} $

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