2x(x+4)=4x+6x(x+5)

Solution for 2x(x+4)=4x+6x(x+5) equation:

2x(x+4)=4x+6x(x+5)

We move all terms to the left:

2x(x+4)-(4x+6x(x+5))=0

We multiply parentheses

2x^2+8x-(4x+6x(x+5))=0


We calculate terms in parentheses: -(4x+6x(x+5)), so:

4x+6x(x+5)

We multiply parentheses

6x^2+4x+30x

We add all the numbers together, and all the variables

6x^2+34x

Back to the equation:

-(6x^2+34x)


We get rid of parentheses

2x^2-6x^2+8x-34x=0

We add all the numbers together, and all the variables

-4x^2-26x=0

a = -4; b = -26; c = 0;
Δ = b2-4ac
Δ = -262-4·(-4)·0
Δ = 676
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{676}=26$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-26)-26}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-26)+26}{2*-4}=\frac{52}{-8}
=-6+1/2
$