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x2-18x-89=0
We add all the numbers together, and all the variables
x^2-18x-89=0
a = 1; b = -18; c = -89;
Δ = b2-4ac
Δ = -182-4·1·(-89)
Δ = 680
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{680}=\sqrt{4*170}=\sqrt{4}*\sqrt{170}=2\sqrt{170}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-2\sqrt{170}}{2*1}=\frac{18-2\sqrt{170}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+2\sqrt{170}}{2*1}=\frac{18+2\sqrt{170}}{2} $
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