(8x-7)(5x+1)=(5x+1)

Solution for (8x-7)(5x+1)=(5x+1) equation:

(8x-7)(5x+1)=(5x+1)

We move all terms to the left:

(8x-7)(5x+1)-((5x+1))=0

We multiply parentheses ..

(+40x^2+8x-35x-7)-((5x+1))=0


We calculate terms in parentheses: -((5x+1)), so:

(5x+1)

We get rid of parentheses

5x+1

Back to the equation:

-(5x+1)


We get rid of parentheses

40x^2+8x-35x-5x-7-1=0

We add all the numbers together, and all the variables

40x^2-32x-8=0

a = 40; b = -32; c = -8;
Δ = b2-4ac
Δ = -322-4·40·(-8)
Δ = 2304
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2304}=48$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-48}{2*40}=\frac{-16}{80}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+48}{2*40}=\frac{80}{80}
=1
$