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-x^2-23x-5=0
We add all the numbers together, and all the variables
-1x^2-23x-5=0
a = -1; b = -23; c = -5;
Δ = b2-4ac
Δ = -232-4·(-1)·(-5)
Δ = 509
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-\sqrt{509}}{2*-1}=\frac{23-\sqrt{509}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+\sqrt{509}}{2*-1}=\frac{23+\sqrt{509}}{-2} $
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