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9x^2+6x+1=16
We move all terms to the left:
9x^2+6x+1-(16)=0
We add all the numbers together, and all the variables
9x^2+6x-15=0
a = 9; b = 6; c = -15;
Δ = b2-4ac
Δ = 62-4·9·(-15)
Δ = 576
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{576}=24$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24}{2*9}=\frac{-30}{18} =-1+2/3 $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24}{2*9}=\frac{18}{18} =1 $
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