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x^2-10x-83=0
a = 1; b = -10; c = -83;
Δ = b2-4ac
Δ = -102-4·1·(-83)
Δ = 432
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-12\sqrt{3}}{2*1}=\frac{10-12\sqrt{3}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+12\sqrt{3}}{2*1}=\frac{10+12\sqrt{3}}{2} $
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