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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2+3x-6=0

a = 2; b = 3; c = -6;
Δ = b2-4ac
Δ = 32-4·2·(-6)
Δ = 57
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{57}}{2*2}=\frac{-3-\sqrt{57}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{57}}{2*2}=\frac{-3+\sqrt{57}}{4}
$