6x(7+2x)=4x(2x-1)

Solution for 6x(7+2x)=4x(2x-1) equation:

6x(7+2x)=4x(2x-1)

We move all terms to the left:

6x(7+2x)-(4x(2x-1))=0

We add all the numbers together, and all the variables

6x(2x+7)-(4x(2x-1))=0

We multiply parentheses

12x^2+42x-(4x(2x-1))=0


We calculate terms in parentheses: -(4x(2x-1)), so:

4x(2x-1)

We multiply parentheses

8x^2-4x

Back to the equation:

-(8x^2-4x)


We get rid of parentheses

12x^2-8x^2+42x+4x=0

We add all the numbers together, and all the variables

4x^2+46x=0

a = 4; b = 46; c = 0;
Δ = b2-4ac
Δ = 462-4·4·0
Δ = 2116
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2116}=46$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(46)-46}{2*4}=\frac{-92}{8}
=-11+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(46)+46}{2*4}=\frac{0}{8}
=0
$