2(2x-3)=x(2x-3)2

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

2(2x-3)=x(2x-3)2

We move all terms to the left:

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

We multiply parentheses

4x-(x(2x-3)2)-6=0


We calculate terms in parentheses: -(x(2x-3)2), so:

x(2x-3)2

We multiply parentheses

4x^2-6x

Back to the equation:

-(4x^2-6x)


We get rid of parentheses

-4x^2+4x+6x-6=0

We add all the numbers together, and all the variables

-4x^2+10x-6=0

a = -4; b = 10; c = -6;
Δ = b2-4ac
Δ = 102-4·(-4)·(-6)
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2}{2*-4}=\frac{-12}{-8}
=1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2}{2*-4}=\frac{-8}{-8}
=1
$