(2x+5)(x-6)=42

Solution for (2x+5)(x-6)=42 equation:

(2x+5)(x-6)=42

We move all terms to the left:

(2x+5)(x-6)-(42)=0

We multiply parentheses ..

(+2x^2-12x+5x-30)-42=0

We get rid of parentheses

2x^2-12x+5x-30-42=0

We add all the numbers together, and all the variables

2x^2-7x-72=0

a = 2; b = -7; c = -72;
Δ = b2-4ac
Δ = -72-4·2·(-72)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-25}{2*2}=\frac{-18}{4}
=-4+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+25}{2*2}=\frac{32}{4}
=8
$