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4x^2-144x-324=0
a = 4; b = -144; c = -324;
Δ = b2-4ac
Δ = -1442-4·4·(-324)
Δ = 25920
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{25920}=\sqrt{5184*5}=\sqrt{5184}*\sqrt{5}=72\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-144)-72\sqrt{5}}{2*4}=\frac{144-72\sqrt{5}}{8} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-144)+72\sqrt{5}}{2*4}=\frac{144+72\sqrt{5}}{8} $
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