x(2x-3)=4x

Solution for x(2x-3)=4x equation:

x(2x-3)=4x

We move all terms to the left:

x(2x-3)-(4x)=0

We add all the numbers together, and all the variables

-4x+x(2x-3)=0

We multiply parentheses

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

We add all the numbers together, and all the variables

2x^2-7x=0

a = 2; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·2·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*2}=\frac{14}{4}
=3+1/2
$