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x^2+44x-10000=0
a = 1; b = 44; c = -10000;
Δ = b2-4ac
Δ = 442-4·1·(-10000)
Δ = 41936
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{41936}=\sqrt{16*2621}=\sqrt{16}*\sqrt{2621}=4\sqrt{2621}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(44)-4\sqrt{2621}}{2*1}=\frac{-44-4\sqrt{2621}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(44)+4\sqrt{2621}}{2*1}=\frac{-44+4\sqrt{2621}}{2} $
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