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

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

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

We move all terms to the left:

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

We multiply parentheses

7x^2-28x-(2x(x+1))=0


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

2x(x+1)

We multiply parentheses

2x^2+2x

Back to the equation:

-(2x^2+2x)


We get rid of parentheses

7x^2-2x^2-28x-2x=0

We add all the numbers together, and all the variables

5x^2-30x=0

a = 5; b = -30; c = 0;
Δ = b2-4ac
Δ = -302-4·5·0
Δ = 900
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{900}=30$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-30)-30}{2*5}=\frac{0}{10}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-30)+30}{2*5}=\frac{60}{10}
=6
$