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x^2-4x-100000=0
a = 1; b = -4; c = -100000;
Δ = b2-4ac
Δ = -42-4·1·(-100000)
Δ = 400016
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{400016}=\sqrt{16*25001}=\sqrt{16}*\sqrt{25001}=4\sqrt{25001}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4\sqrt{25001}}{2*1}=\frac{4-4\sqrt{25001}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4\sqrt{25001}}{2*1}=\frac{4+4\sqrt{25001}}{2} $
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