9x=7x(x+2)

Solution for 9x=7x(x+2) equation:

9x=7x(x+2)

We move all terms to the left:

9x-(7x(x+2))=0


We calculate terms in parentheses: -(7x(x+2)), so:

7x(x+2)

We multiply parentheses

7x^2+14x

Back to the equation:

-(7x^2+14x)


We get rid of parentheses

-7x^2+9x-14x=0

We add all the numbers together, and all the variables

-7x^2-5x=0

a = -7; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-7)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-7}=\frac{10}{-14}
=-5/7
$