2x+3x(x-4)=x(5+7x)

Solution for 2x+3x(x-4)=x(5+7x) equation:

2x+3x(x-4)=x(5+7x)

We move all terms to the left:

2x+3x(x-4)-(x(5+7x))=0

We add all the numbers together, and all the variables

2x+3x(x-4)-(x(7x+5))=0

We multiply parentheses

3x^2+2x-12x-(x(7x+5))=0


We calculate terms in parentheses: -(x(7x+5)), so:

x(7x+5)

We multiply parentheses

7x^2+5x

Back to the equation:

-(7x^2+5x)


We add all the numbers together, and all the variables

3x^2-10x-(7x^2+5x)=0

We get rid of parentheses

3x^2-7x^2-10x-5x=0

We add all the numbers together, and all the variables

-4x^2-15x=0

a = -4; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-4)·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-4}=\frac{30}{-8}
=-3+3/4
$