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

Solution for -2x(x-3)+6x=2x+3(x-4) equation:

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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


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

2x+3(x-4)

We multiply parentheses

2x+3x-12

We add all the numbers together, and all the variables

5x-12

Back to the equation:

-(5x-12)


We add all the numbers together, and all the variables

-2x^2+12x-(5x-12)=0

We get rid of parentheses

-2x^2+12x-5x+12=0

We add all the numbers together, and all the variables

-2x^2+7x+12=0

a = -2; b = 7; c = +12;
Δ = b2-4ac
Δ = 72-4·(-2)·12
Δ = 145
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{-(7)-\sqrt{145}}{2*-2}=\frac{-7-\sqrt{145}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{145}}{2*-2}=\frac{-7+\sqrt{145}}{-4}
$