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12x^2-180x+170=0
a = 12; b = -180; c = +170;
Δ = b2-4ac
Δ = -1802-4·12·170
Δ = 24240
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{24240}=\sqrt{16*1515}=\sqrt{16}*\sqrt{1515}=4\sqrt{1515}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-180)-4\sqrt{1515}}{2*12}=\frac{180-4\sqrt{1515}}{24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-180)+4\sqrt{1515}}{2*12}=\frac{180+4\sqrt{1515}}{24} $
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