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x^2+2x-11/9=0
We multiply all the terms by the denominator
x^2*9+2x*9-11=0
Wy multiply elements
9x^2+18x-11=0
a = 9; b = 18; c = -11;
Δ = b2-4ac
Δ = 182-4·9·(-11)
Δ = 720
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{720}=\sqrt{144*5}=\sqrt{144}*\sqrt{5}=12\sqrt{5}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-12\sqrt{5}}{2*9}=\frac{-18-12\sqrt{5}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+12\sqrt{5}}{2*9}=\frac{-18+12\sqrt{5}}{18} $
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