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16x^2-200x+16=0
a = 16; b = -200; c = +16;
Δ = b2-4ac
Δ = -2002-4·16·16
Δ = 38976
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{38976}=\sqrt{64*609}=\sqrt{64}*\sqrt{609}=8\sqrt{609}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-200)-8\sqrt{609}}{2*16}=\frac{200-8\sqrt{609}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-200)+8\sqrt{609}}{2*16}=\frac{200+8\sqrt{609}}{32} $
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