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9x^2-8x=11
We move all terms to the left:
9x^2-8x-(11)=0
a = 9; b = -8; c = -11;
Δ = b2-4ac
Δ = -82-4·9·(-11)
Δ = 460
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{460}=\sqrt{4*115}=\sqrt{4}*\sqrt{115}=2\sqrt{115}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-2\sqrt{115}}{2*9}=\frac{8-2\sqrt{115}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+2\sqrt{115}}{2*9}=\frac{8+2\sqrt{115}}{18} $
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