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9x^2+51x-84=0
a = 9; b = 51; c = -84;
Δ = b2-4ac
Δ = 512-4·9·(-84)
Δ = 5625
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{5625}=75$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-75}{2*9}=\frac{-126}{18} =-7 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+75}{2*9}=\frac{24}{18} =1+1/3 $
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