Eq1

When the product of two less than three times a number and four is subtracted from nine times the number, the result is eight more than five times the number.

What is the number?

Correct answer:

x₁ =  1.2963

Step-by-step explanation:

$$\begin{gathered} (9x-4)\cdot (3x-2)=8+5x \\ (9x-4)\cdot (3x-2)=8+5x \\ 27x^2-35x=0 \\ a=27;b=-35;c=0 \\ D=b^2-4ac=35^2-4\cdot 27\cdot 0=1225 \\ D>0 \\ {x}_{1,2}=\frac{-b\pm \sqrt{D}}{2a}=\frac{35\pm \sqrt{1225}}{54} \\ {x}_{1,2}=\frac{35\pm 35}{54} \\ {x}_{1,2}=0.648148\pm 0.648148 \\ {x}_1=1.296296296=1.2963 \\ {x}_2=0 \end{gathered}$$

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