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44x^2-120x-84=0
a = 44; b = -120; c = -84;
Δ = b2-4ac
Δ = -1202-4·44·(-84)
Δ = 29184
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{29184}=\sqrt{256*114}=\sqrt{256}*\sqrt{114}=16\sqrt{114}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-16\sqrt{114}}{2*44}=\frac{120-16\sqrt{114}}{88} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+16\sqrt{114}}{2*44}=\frac{120+16\sqrt{114}}{88} $
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