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5=100+64x-16x^2
We move all terms to the left:
5-(100+64x-16x^2)=0
We get rid of parentheses
16x^2-64x-100+5=0
We add all the numbers together, and all the variables
16x^2-64x-95=0
a = 16; b = -64; c = -95;
Δ = b2-4ac
Δ = -642-4·16·(-95)
Δ = 10176
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{10176}=\sqrt{64*159}=\sqrt{64}*\sqrt{159}=8\sqrt{159}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{159}}{2*16}=\frac{64-8\sqrt{159}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{159}}{2*16}=\frac{64+8\sqrt{159}}{32} $
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