10x^2-100x+9=0

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Solution for 10x^2-100x+9=0 equation:



10x^2-100x+9=0
a = 10; b = -100; c = +9;
Δ = b2-4ac
Δ = -1002-4·10·9
Δ = 9640
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:
$\sqrt{\Delta}=\sqrt{9640}=\sqrt{4*2410}=\sqrt{4}*\sqrt{2410}=2\sqrt{2410}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-100)-2\sqrt{2410}}{2*10}=\frac{100-2\sqrt{2410}}{20} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-100)+2\sqrt{2410}}{2*10}=\frac{100+2\sqrt{2410}}{20} $

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