(x+1)(3x-1)-(5x+1)=0

Solution for (x+1)(3x-1)-(5x+1)=0 equation:

(x+1)(3x-1)-(5x+1)=0

We get rid of parentheses

(x+1)(3x-1)-5x-1=0

We multiply parentheses ..

(+3x^2-1x+3x-1)-5x-1=0

We get rid of parentheses

3x^2-1x+3x-5x-1-1=0

We add all the numbers together, and all the variables

3x^2-3x-2=0

a = 3; b = -3; c = -2;
Δ = b2-4ac
Δ = -32-4·3·(-2)
Δ = 33
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-\sqrt{33}}{2*3}=\frac{3-\sqrt{33}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{33}}{2*3}=\frac{3+\sqrt{33}}{6}
$