x2-14x+21=0

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Solution for x2-14x+21=0 equation:



x2-14x+21=0
We add all the numbers together, and all the variables
x^2-14x+21=0
a = 1; b = -14; c = +21;
Δ = b2-4ac
Δ = -142-4·1·21
Δ = 112
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:
$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-4\sqrt{7}}{2*1}=\frac{14-4\sqrt{7}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+4\sqrt{7}}{2*1}=\frac{14+4\sqrt{7}}{2} $

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