(5x+1)(x-2)=(5x+1)

Solution for (5x+1)(x-2)=(5x+1) equation:

(5x+1)(x-2)=(5x+1)

We move all terms to the left:

(5x+1)(x-2)-((5x+1))=0

We multiply parentheses ..

(+5x^2-10x+x-2)-((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

5x^2-10x+x-5x-2-1=0

We add all the numbers together, and all the variables

5x^2-14x-3=0

a = 5; b = -14; c = -3;
Δ = b2-4ac
Δ = -142-4·5·(-3)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-16}{2*5}=\frac{-2}{10}
=-1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+16}{2*5}=\frac{30}{10}
=3
$