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x2-3x-27=0
We add all the numbers together, and all the variables
x^2-3x-27=0
a = 1; b = -3; c = -27;
Δ = b2-4ac
Δ = -32-4·1·(-27)
Δ = 117
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{117}=\sqrt{9*13}=\sqrt{9}*\sqrt{13}=3\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-3\sqrt{13}}{2*1}=\frac{3-3\sqrt{13}}{2} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+3\sqrt{13}}{2*1}=\frac{3+3\sqrt{13}}{2} $
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