2(2x-1)=2(x+1)(3/2)

Solution for 2(2x-1)=2(x+1)(3/2) equation:

2(2x-1)=2(x+1)(3/2)

We move all terms to the left:

2(2x-1)-(2(x+1)(3/2))=0

We add all the numbers together, and all the variables

2(2x-1)-(2(x+1)(+3/2))=0

We multiply parentheses

4x-(2(x+1)(+3/2))-2=0

We multiply parentheses ..

-(2(+3x^2+1*3/2))+4x-2=0

We multiply all the terms by the denominator


-(2(+3x^2+1*3+4x*2))-2*2))=0


We calculate terms in parentheses: -(2(+3x^2+1*3+4x*2)), so:

2(+3x^2+1*3+4x*2)

We multiply parentheses

6x^2+16x+6

Back to the equation:

-(6x^2+16x+6)


We add all the numbers together, and all the variables

-(6x^2+16x+6)=0

We get rid of parentheses

-6x^2-16x-6=0

a = -6; b = -16; c = -6;
Δ = b2-4ac
Δ = -162-4·(-6)·(-6)
Δ = 112
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-16)-4\sqrt{7}}{2*-6}=\frac{16-4\sqrt{7}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-16)+4\sqrt{7}}{2*-6}=\frac{16+4\sqrt{7}}{-12}
$