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

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

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

We move all terms to the left:

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

We multiply parentheses

2x^2-8x-(x(3x+7))=0


We calculate terms in parentheses: -(x(3x+7)), so:

x(3x+7)

We multiply parentheses

3x^2+7x

Back to the equation:

-(3x^2+7x)


We get rid of parentheses

2x^2-3x^2-8x-7x=0

We add all the numbers together, and all the variables

-1x^2-15x=0

a = -1; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·(-1)·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*-1}=\frac{0}{-2}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*-1}=\frac{30}{-2}
=-15
$