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7x^2-21x+7=0
a = 7; b = -21; c = +7;
Δ = b2-4ac
Δ = -212-4·7·7
Δ = 245
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{245}=\sqrt{49*5}=\sqrt{49}*\sqrt{5}=7\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-7\sqrt{5}}{2*7}=\frac{21-7\sqrt{5}}{14} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+7\sqrt{5}}{2*7}=\frac{21+7\sqrt{5}}{14} $
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