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9x^2+3=11
We move all terms to the left:
9x^2+3-(11)=0
We add all the numbers together, and all the variables
9x^2-8=0
a = 9; b = 0; c = -8;
Δ = b2-4ac
Δ = 02-4·9·(-8)
Δ = 288
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{288}=\sqrt{144*2}=\sqrt{144}*\sqrt{2}=12\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{2}}{2*9}=\frac{0-12\sqrt{2}}{18} =-\frac{12\sqrt{2}}{18} =-\frac{2\sqrt{2}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{2}}{2*9}=\frac{0+12\sqrt{2}}{18} =\frac{12\sqrt{2}}{18} =\frac{2\sqrt{2}}{3} $
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