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16x^2-144x+107=0
a = 16; b = -144; c = +107;
Δ = b2-4ac
Δ = -1442-4·16·107
Δ = 13888
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{13888}=\sqrt{64*217}=\sqrt{64}*\sqrt{217}=8\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-8\sqrt{217}}{2*16}=\frac{144-8\sqrt{217}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+8\sqrt{217}}{2*16}=\frac{144+8\sqrt{217}}{32} $
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