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(12x^2)-92x-120=0
a = 12; b = -92; c = -120;
Δ = b2-4ac
Δ = -922-4·12·(-120)
Δ = 14224
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{14224}=\sqrt{16*889}=\sqrt{16}*\sqrt{889}=4\sqrt{889}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-92)-4\sqrt{889}}{2*12}=\frac{92-4\sqrt{889}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-92)+4\sqrt{889}}{2*12}=\frac{92+4\sqrt{889}}{24} $
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