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234-31x-x^2-66=0
We add all the numbers together, and all the variables
-1x^2-31x+168=0
a = -1; b = -31; c = +168;
Δ = b2-4ac
Δ = -312-4·(-1)·168
Δ = 1633
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{-(-31)-\sqrt{1633}}{2*-1}=\frac{31-\sqrt{1633}}{-2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-31)+\sqrt{1633}}{2*-1}=\frac{31+\sqrt{1633}}{-2} $
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