# Solve Equation

Algebra

### Solve Equation

(x - 3b) / c = 9(c - b) / x

Solve.

x^2 - 3bx = 9c^2 - bc Cross multiplied.

Not sure how to proceed.
Guest

### Re: Solve Equation

Good afternoon!

$$\frac{x-3b}{c}=\frac{9(c-b)}{x}\\ x(x-3b)=9c(c-b)\\ x^2-3bx=9c^2-9bc\\ x^2-3bx-9c^2+9bc=0\\ \Delta=(-3b)^2-4(1)(-9c^2+9bc)\\ \Delta=9b^2+36c^2-36bc=9\left(b^2-4bc+4c^2\right)=9\left(b-2c\right)^2\\ x=\frac{-(-3b)\pm\sqrt{\Delta}}{2(1)}\\ x=\frac{3b\pm 3(b-2c)}{2}\\ x'=\frac{3b+3b-6c}{2}=3(b-c)\\ x''=\frac{3b-3b+6c}{2}=3c$$

Hope to Have Helped (3H)

Baltuilhe

Posts: 94
Joined: Fri Dec 14, 2018 3:55 pm
Reputation: 58

### Re: Solve Equation

I don't understand your two steps that begin with the triangles.
Guest

### Re: Solve Equation

Good afternoon!

It's the solution to 2nd degree equation:
$$ax^2+bx+c=0\Rightarrow \begin{cases}\Delta=b^2-4ac\\ x=\frac{-b\pm\sqrt{\Delta}}{2a}\Rightarrow\begin{cases}x'=\frac{-b+\sqrt{\Delta}}{2a}\\x''=\frac{-b-\sqrt{\Delta}}{2a}\end{cases} \end{cases}$$

See?

Baltuilhe

Posts: 94
Joined: Fri Dec 14, 2018 3:55 pm
Reputation: 58

### Re: Solve Equation

Good Afternoon!

Ok, Thanks again.
Guest

### Re: Solve Equation

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Guest