(x+7)(2x-3)=1

Solution for (x+7)(2x-3)=1 equation:

(x+7)(2x-3)=1

We move all terms to the left:

(x+7)(2x-3)-(1)=0

We multiply parentheses ..

(+2x^2-3x+14x-21)-1=0

We get rid of parentheses

2x^2-3x+14x-21-1=0

We add all the numbers together, and all the variables

2x^2+11x-22=0

a = 2; b = 11; c = -22;
Δ = b2-4ac
Δ = 112-4·2·(-22)
Δ = 297
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-3\sqrt{33}}{2*2}=\frac{-11-3\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+3\sqrt{33}}{2*2}=\frac{-11+3\sqrt{33}}{4}
$