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9x^2-144x-285=0
a = 9; b = -144; c = -285;
Δ = b2-4ac
Δ = -1442-4·9·(-285)
Δ = 30996
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{30996}=\sqrt{36*861}=\sqrt{36}*\sqrt{861}=6\sqrt{861}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-6\sqrt{861}}{2*9}=\frac{144-6\sqrt{861}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+6\sqrt{861}}{2*9}=\frac{144+6\sqrt{861}}{18} $
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