(2x+3)(x-6)=5

Solution for (2x+3)(x-6)=5 equation:

(2x+3)(x-6)=5

We move all terms to the left:

(2x+3)(x-6)-(5)=0

We multiply parentheses ..

(+2x^2-12x+3x-18)-5=0

We get rid of parentheses

2x^2-12x+3x-18-5=0

We add all the numbers together, and all the variables

2x^2-9x-23=0

a = 2; b = -9; c = -23;
Δ = b2-4ac
Δ = -92-4·2·(-23)
Δ = 265
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{-(-9)-\sqrt{265}}{2*2}=\frac{9-\sqrt{265}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{265}}{2*2}=\frac{9+\sqrt{265}}{4}
$