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9x^2-1=872
We move all terms to the left:
9x^2-1-(872)=0
We add all the numbers together, and all the variables
9x^2-873=0
a = 9; b = 0; c = -873;
Δ = b2-4ac
Δ = 02-4·9·(-873)
Δ = 31428
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{31428}=\sqrt{324*97}=\sqrt{324}*\sqrt{97}=18\sqrt{97}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-18\sqrt{97}}{2*9}=\frac{0-18\sqrt{97}}{18} =-\frac{18\sqrt{97}}{18} =-\sqrt{97} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+18\sqrt{97}}{2*9}=\frac{0+18\sqrt{97}}{18} =\frac{18\sqrt{97}}{18} =\sqrt{97} $
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