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1-2x+16x^2=8.2
We move all terms to the left:
1-2x+16x^2-(8.2)=0
We add all the numbers together, and all the variables
16x^2-2x-7.2=0
a = 16; b = -2; c = -7.2;
Δ = b2-4ac
Δ = -22-4·16·(-7.2)
Δ = 464.8
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{-(-2)-\sqrt{464.8}}{2*16}=\frac{2-\sqrt{464.8}}{32} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+\sqrt{464.8}}{2*16}=\frac{2+\sqrt{464.8}}{32} $
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