3x=4x(x-2.25)

Solution for 3x=4x(x-2.25) equation:

3x=4x(x-2.25)

We move all terms to the left:

3x-(4x(x-2.25))=0


We calculate terms in parentheses: -(4x(x-2.25)), so:

4x(x-2.25)

We multiply parentheses

4x^2-9x

Back to the equation:

-(4x^2-9x)


We get rid of parentheses

-4x^2+3x+9x=0

We add all the numbers together, and all the variables

-4x^2+12x=0

a = -4; b = 12; c = 0;
Δ = b2-4ac
Δ = 122-4·(-4)·0
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-12}{2*-4}=\frac{-24}{-8}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+12}{2*-4}=\frac{0}{-8}
=0
$