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9x^2-96=81
We move all terms to the left:
9x^2-96-(81)=0
We add all the numbers together, and all the variables
9x^2-177=0
a = 9; b = 0; c = -177;
Δ = b2-4ac
Δ = 02-4·9·(-177)
Δ = 6372
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{6372}=\sqrt{36*177}=\sqrt{36}*\sqrt{177}=6\sqrt{177}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{177}}{2*9}=\frac{0-6\sqrt{177}}{18} =-\frac{6\sqrt{177}}{18} =-\frac{\sqrt{177}}{3} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{177}}{2*9}=\frac{0+6\sqrt{177}}{18} =\frac{6\sqrt{177}}{18} =\frac{\sqrt{177}}{3} $
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