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

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

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

We move all terms to the left:

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

We multiply parentheses

-2x^2-6x-(4(x-1))=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 get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = -10; c = +4;
Δ = b2-4ac
Δ = -102-4·(-2)·4
Δ = 132
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:

$\sqrt{\Delta}=\sqrt{132}=\sqrt{4*33}=\sqrt{4}*\sqrt{33}=2\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{33}}{2*-2}=\frac{10-2\sqrt{33}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{33}}{2*-2}=\frac{10+2\sqrt{33}}{-4}
$