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36x^2-9x-105=0
a = 36; b = -9; c = -105;
Δ = b2-4ac
Δ = -92-4·36·(-105)
Δ = 15201
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{15201}=\sqrt{9*1689}=\sqrt{9}*\sqrt{1689}=3\sqrt{1689}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-3\sqrt{1689}}{2*36}=\frac{9-3\sqrt{1689}}{72} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+3\sqrt{1689}}{2*36}=\frac{9+3\sqrt{1689}}{72} $
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