5x=7x(x+2)

Solution for 5x=7x(x+2) equation:

5x=7x(x+2)

We move all terms to the left:

5x-(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+5x-14x=0

We add all the numbers together, and all the variables

-7x^2-9x=0

a = -7; b = -9; c = 0;
Δ = b2-4ac
Δ = -92-4·(-7)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-9}{2*-7}=\frac{0}{-14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+9}{2*-7}=\frac{18}{-14}
=-1+2/7
$