2(3x-1)=-4x(x-7)

Solution for 2(3x-1)=-4x(x-7) equation:

2(3x-1)=-4x(x-7)

We move all terms to the left:

2(3x-1)-(-4x(x-7))=0

We multiply parentheses

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


We calculate terms in parentheses: -(-4x(x-7)), so:

-4x(x-7)

We multiply parentheses

-4x^2+28x

Back to the equation:

-(-4x^2+28x)


We get rid of parentheses

4x^2-28x+6x-2=0

We add all the numbers together, and all the variables

4x^2-22x-2=0

a = 4; b = -22; c = -2;
Δ = b2-4ac
Δ = -222-4·4·(-2)
Δ = 516
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:

$\sqrt{\Delta}=\sqrt{516}=\sqrt{4*129}=\sqrt{4}*\sqrt{129}=2\sqrt{129}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-22)-2\sqrt{129}}{2*4}=\frac{22-2\sqrt{129}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-22)+2\sqrt{129}}{2*4}=\frac{22+2\sqrt{129}}{8}
$