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X2+3X+13/9=0
We add all the numbers together, and all the variables
X^2+3X+13/9=0
We multiply all the terms by the denominator
X^2*9+3X*9+13=0
Wy multiply elements
9X^2+27X+13=0
a = 9; b = 27; c = +13;
Δ = b2-4ac
Δ = 272-4·9·13
Δ = 261
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{261}=\sqrt{9*29}=\sqrt{9}*\sqrt{29}=3\sqrt{29}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{29}}{2*9}=\frac{-27-3\sqrt{29}}{18} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{29}}{2*9}=\frac{-27+3\sqrt{29}}{18} $
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