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x2-4x-213=0
We add all the numbers together, and all the variables
x^2-4x-213=0
a = 1; b = -4; c = -213;
Δ = b2-4ac
Δ = -42-4·1·(-213)
Δ = 868
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{868}=\sqrt{4*217}=\sqrt{4}*\sqrt{217}=2\sqrt{217}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{217}}{2*1}=\frac{4-2\sqrt{217}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{217}}{2*1}=\frac{4+2\sqrt{217}}{2} $
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