9x=3x(3x-7)

Solution for 9x=3x(3x-7) equation:

9x=3x(3x-7)

We move all terms to the left:

9x-(3x(3x-7))=0


We calculate terms in parentheses: -(3x(3x-7)), so:

3x(3x-7)

We multiply parentheses

9x^2-21x

Back to the equation:

-(9x^2-21x)


We get rid of parentheses

-9x^2+9x+21x=0

We add all the numbers together, and all the variables

-9x^2+30x=0

a = -9; b = 30; c = 0;
Δ = b2-4ac
Δ = 302-4·(-9)·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-30}{2*-9}=\frac{-60}{-18}
=3+1/3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+30}{2*-9}=\frac{0}{-18}
=0
$