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3x(x-9)-2=-35
We move all terms to the left:
3x(x-9)-2-(-35)=0
We add all the numbers together, and all the variables
3x(x-9)+33=0
We multiply parentheses
3x^2-27x+33=0
a = 3; b = -27; c = +33;
Δ = b2-4ac
Δ = -272-4·3·33
Δ = 333
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}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{333}=\sqrt{9*37}=\sqrt{9}*\sqrt{37}=3\sqrt{37}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-27)-3\sqrt{37}}{2*3}=\frac{27-3\sqrt{37}}{6} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-27)+3\sqrt{37}}{2*3}=\frac{27+3\sqrt{37}}{6} $
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