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9x^2+21x=8
We move all terms to the left:
9x^2+21x-(8)=0
a = 9; b = 21; c = -8;
Δ = b2-4ac
Δ = 212-4·9·(-8)
Δ = 729
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{729}=27$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(21)-27}{2*9}=\frac{-48}{18} =-2+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(21)+27}{2*9}=\frac{6}{18} =1/3 $
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