(2x-1)(x+3)-1=2x+1

Solution for (2x-1)(x+3)-1=2x+1 equation:

(2x-1)(x+3)-1=2x+1

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

(+2x^2+6x-1x-3)-2x-1-1=0

We add all the numbers together, and all the variables

(+2x^2+6x-1x-3)-2x-2=0

We get rid of parentheses

2x^2+6x-1x-2x-3-2=0

We add all the numbers together, and all the variables

2x^2+3x-5=0

a = 2; b = 3; c = -5;
Δ = b2-4ac
Δ = 32-4·2·(-5)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-7}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+7}{2*2}=\frac{4}{4}
=1
$