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9x^2-66x=121
We move all terms to the left:
9x^2-66x-(121)=0
a = 9; b = -66; c = -121;
Δ = b2-4ac
Δ = -662-4·9·(-121)
Δ = 8712
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{8712}=\sqrt{4356*2}=\sqrt{4356}*\sqrt{2}=66\sqrt{2}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-66)-66\sqrt{2}}{2*9}=\frac{66-66\sqrt{2}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-66)+66\sqrt{2}}{2*9}=\frac{66+66\sqrt{2}}{18} $
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