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

Solution for x(2x-3)-2(3+2x)=-4(x-1) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

2x^2-3x-4x-(-4(x-1))-6=0


We calculate terms in parentheses: -(-4(x-1)), so:

-4(x-1)

We multiply parentheses

-4x+4

Back to the equation:

-(-4x+4)


We add all the numbers together, and all the variables

2x^2-7x-(-4x+4)-6=0

We get rid of parentheses

2x^2-7x+4x-4-6=0

We add all the numbers together, and all the variables

2x^2-3x-10=0

a = 2; b = -3; c = -10;
Δ = b2-4ac
Δ = -32-4·2·(-10)
Δ = 89
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{89}}{2*2}=\frac{3-\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{89}}{2*2}=\frac{3+\sqrt{89}}{4}
$