(2x-9)(x-2)=42

Solution for (2x-9)(x-2)=42 equation:

(2x-9)(x-2)=42

We move all terms to the left:

(2x-9)(x-2)-(42)=0

We multiply parentheses ..

(+2x^2-4x-9x+18)-42=0

We get rid of parentheses

2x^2-4x-9x+18-42=0

We add all the numbers together, and all the variables

2x^2-13x-24=0

a = 2; b = -13; c = -24;
Δ = b2-4ac
Δ = -132-4·2·(-24)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-19}{2*2}=\frac{-6}{4}
=-1+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+19}{2*2}=\frac{32}{4}
=8
$