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12x^2-120x+144=0
a = 12; b = -120; c = +144;
Δ = b2-4ac
Δ = -1202-4·12·144
Δ = 7488
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{7488}=\sqrt{576*13}=\sqrt{576}*\sqrt{13}=24\sqrt{13}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-120)-24\sqrt{13}}{2*12}=\frac{120-24\sqrt{13}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-120)+24\sqrt{13}}{2*12}=\frac{120+24\sqrt{13}}{24} $
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