15x=20x(x-2)

Solution for 15x=20x(x-2) equation:

15x=20x(x-2)

We move all terms to the left:

15x-(20x(x-2))=0


We calculate terms in parentheses: -(20x(x-2)), so:

20x(x-2)

We multiply parentheses

20x^2-40x

Back to the equation:

-(20x^2-40x)


We get rid of parentheses

-20x^2+15x+40x=0

We add all the numbers together, and all the variables

-20x^2+55x=0

a = -20; b = 55; c = 0;
Δ = b2-4ac
Δ = 552-4·(-20)·0
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-55}{2*-20}=\frac{-110}{-40}
=2+3/4
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+55}{2*-20}=\frac{0}{-40}
=0
$