(2x+3)(x+6)=1

Solution for (2x+3)(x+6)=1 equation:

(2x+3)(x+6)=1

We move all terms to the left:

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

We multiply parentheses ..

(+2x^2+12x+3x+18)-1=0

We get rid of parentheses

2x^2+12x+3x+18-1=0

We add all the numbers together, and all the variables

2x^2+15x+17=0

a = 2; b = 15; c = +17;
Δ = b2-4ac
Δ = 152-4·2·17
Δ = 89
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{-(15)-\sqrt{89}}{2*2}=\frac{-15-\sqrt{89}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{89}}{2*2}=\frac{-15+\sqrt{89}}{4}
$