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-12x^2+35x+1=0
a = -12; b = 35; c = +1;
Δ = b2-4ac
Δ = 352-4·(-12)·1
Δ = 1273
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(35)-\sqrt{1273}}{2*-12}=\frac{-35-\sqrt{1273}}{-24} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(35)+\sqrt{1273}}{2*-12}=\frac{-35+\sqrt{1273}}{-24} $
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