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

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

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

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2+8x-1x-4)-(x(x+7))=0


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

x(x+7)

We multiply parentheses

x^2+7x

Back to the equation:

-(x^2+7x)


We get rid of parentheses

2x^2-x^2+8x-1x-7x-4=0

We add all the numbers together, and all the variables

x^2-4=0

a = 1; b = 0; c = -4;
Δ = b2-4ac
Δ = 02-4·1·(-4)
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4}{2*1}=\frac{-4}{2}
=-2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4}{2*1}=\frac{4}{2}
=2
$