2(-3x-1)=-2(x-2)(x+7)

Solution for 2(-3x-1)=-2(x-2)(x+7) equation:

2(-3x-1)=-2(x-2)(x+7)

We move all terms to the left:

2(-3x-1)-(-2(x-2)(x+7))=0

We multiply parentheses

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

We multiply parentheses ..

-(-2(+x^2+7x-2x-14))-6x-2=0


We calculate terms in parentheses: -(-2(+x^2+7x-2x-14)), so:

-2(+x^2+7x-2x-14)

We multiply parentheses

-2x^2-14x+4x+28

We add all the numbers together, and all the variables

-2x^2-10x+28

Back to the equation:

-(-2x^2-10x+28)


We get rid of parentheses

2x^2+10x-6x-28-2=0

We add all the numbers together, and all the variables

2x^2+4x-30=0

a = 2; b = 4; c = -30;
Δ = b2-4ac
Δ = 42-4·2·(-30)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-16}{2*2}=\frac{-20}{4}
=-5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+16}{2*2}=\frac{12}{4}
=3
$