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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+x-4=0

a = 2; b = 1; c = -4;
Δ = b2-4ac
Δ = 12-4·2·(-4)
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{-(1)-\sqrt{33}}{2*2}=\frac{-1-\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{33}}{2*2}=\frac{-1+\sqrt{33}}{4}
$