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9x^2+6x+1=48
We move all terms to the left:
9x^2+6x+1-(48)=0
We add all the numbers together, and all the variables
9x^2+6x-47=0
a = 9; b = 6; c = -47;
Δ = b2-4ac
Δ = 62-4·9·(-47)
Δ = 1728
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-24\sqrt{3}}{2*9}=\frac{-6-24\sqrt{3}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+24\sqrt{3}}{2*9}=\frac{-6+24\sqrt{3}}{18} $
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