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x^2-55x+430=0
a = 1; b = -55; c = +430;
Δ = b2-4ac
Δ = -552-4·1·430
Δ = 1305
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1305}=\sqrt{9*145}=\sqrt{9}*\sqrt{145}=3\sqrt{145}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-3\sqrt{145}}{2*1}=\frac{55-3\sqrt{145}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+3\sqrt{145}}{2*1}=\frac{55+3\sqrt{145}}{2} $
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