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5x^2-55x+25=0
a = 5; b = -55; c = +25;
Δ = b2-4ac
Δ = -552-4·5·25
Δ = 2525
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2525}=\sqrt{25*101}=\sqrt{25}*\sqrt{101}=5\sqrt{101}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{101}}{2*5}=\frac{55-5\sqrt{101}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{101}}{2*5}=\frac{55+5\sqrt{101}}{10} $
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