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X(3X-9)=38
We move all terms to the left:
X(3X-9)-(38)=0
We multiply parentheses
3X^2-9X-38=0
a = 3; b = -9; c = -38;
Δ = b2-4ac
Δ = -92-4·3·(-38)
Δ = 537
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}$$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{537}}{2*3}=\frac{9-\sqrt{537}}{6} $$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{537}}{2*3}=\frac{9+\sqrt{537}}{6} $
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