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9(x-9)(x-1)=119
We move all terms to the left:
9(x-9)(x-1)-(119)=0
We multiply parentheses ..
9(+x^2-1x-9x+9)-119=0
We multiply parentheses
9x^2-9x-81x+81-119=0
We add all the numbers together, and all the variables
9x^2-90x-38=0
a = 9; b = -90; c = -38;
Δ = b2-4ac
Δ = -902-4·9·(-38)
Δ = 9468
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{9468}=\sqrt{36*263}=\sqrt{36}*\sqrt{263}=6\sqrt{263}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-90)-6\sqrt{263}}{2*9}=\frac{90-6\sqrt{263}}{18} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-90)+6\sqrt{263}}{2*9}=\frac{90+6\sqrt{263}}{18} $
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