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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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


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

(2x+1)(x-1)

We multiply parentheses ..

(+2x^2-2x+x-1)

We get rid of parentheses

2x^2-2x+x-1

We add all the numbers together, and all the variables

2x^2-1x-1

Back to the equation:

-(2x^2-1x-1)


We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2+7x-6=0

a = -1; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·(-1)·(-6)
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-5}{2*-1}=\frac{-12}{-2}
=+6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+5}{2*-1}=\frac{-2}{-2}
=1
$