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9x^2=18+11=29
We move all terms to the left:
9x^2-(18+11)=0
We add all the numbers together, and all the variables
9x^2-29=0
a = 9; b = 0; c = -29;
Δ = b2-4ac
Δ = 02-4·9·(-29)
Δ = 1044
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1044}=\sqrt{36*29}=\sqrt{36}*\sqrt{29}=6\sqrt{29}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{29}}{2*9}=\frac{0-6\sqrt{29}}{18} =-\frac{6\sqrt{29}}{18} =-\frac{\sqrt{29}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{29}}{2*9}=\frac{0+6\sqrt{29}}{18} =\frac{6\sqrt{29}}{18} =\frac{\sqrt{29}}{3} $
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