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-6f^2-5f+9=0
a = -6; b = -5; c = +9;
Δ = b2-4ac
Δ = -52-4·(-6)·9
Δ = 241
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$f_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-\sqrt{241}}{2*-6}=\frac{5-\sqrt{241}}{-12} $$f_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{241}}{2*-6}=\frac{5+\sqrt{241}}{-12} $
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