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-24x^2-5x+1=0
a = -24; b = -5; c = +1;
Δ = b2-4ac
Δ = -52-4·(-24)·1
Δ = 121
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$\sqrt{\Delta}=\sqrt{121}=11$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-11}{2*-24}=\frac{-6}{-48} =1/8 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+11}{2*-24}=\frac{16}{-48} =-1/3 $
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