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5x^2-55x+10=0
a = 5; b = -55; c = +10;
Δ = b2-4ac
Δ = -552-4·5·10
Δ = 2825
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{2825}=\sqrt{25*113}=\sqrt{25}*\sqrt{113}=5\sqrt{113}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-55)-5\sqrt{113}}{2*5}=\frac{55-5\sqrt{113}}{10} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-55)+5\sqrt{113}}{2*5}=\frac{55+5\sqrt{113}}{10} $
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