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144x^2+120x-55=0
a = 144; b = 120; c = -55;
Δ = b2-4ac
Δ = 1202-4·144·(-55)
Δ = 46080
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{46080}=\sqrt{9216*5}=\sqrt{9216}*\sqrt{5}=96\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-96\sqrt{5}}{2*144}=\frac{-120-96\sqrt{5}}{288} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+96\sqrt{5}}{2*144}=\frac{-120+96\sqrt{5}}{288} $
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