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24-14x-x^2=0
We add all the numbers together, and all the variables
-1x^2-14x+24=0
a = -1; b = -14; c = +24;
Δ = b2-4ac
Δ = -142-4·(-1)·24
Δ = 292
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{292}=\sqrt{4*73}=\sqrt{4}*\sqrt{73}=2\sqrt{73}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{73}}{2*-1}=\frac{14-2\sqrt{73}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{73}}{2*-1}=\frac{14+2\sqrt{73}}{-2} $
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