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12x^2-144x-288=0
a = 12; b = -144; c = -288;
Δ = b2-4ac
Δ = -1442-4·12·(-288)
Δ = 34560
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{34560}=\sqrt{2304*15}=\sqrt{2304}*\sqrt{15}=48\sqrt{15}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-48\sqrt{15}}{2*12}=\frac{144-48\sqrt{15}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+48\sqrt{15}}{2*12}=\frac{144+48\sqrt{15}}{24} $
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