(2x+3)(x-2)=44

Solution for (2x+3)(x-2)=44 equation:

(2x+3)(x-2)=44

We move all terms to the left:

(2x+3)(x-2)-(44)=0

We multiply parentheses ..

(+2x^2-4x+3x-6)-44=0

We get rid of parentheses

2x^2-4x+3x-6-44=0

We add all the numbers together, and all the variables

2x^2-1x-50=0

a = 2; b = -1; c = -50;
Δ = b2-4ac
Δ = -12-4·2·(-50)
Δ = 401
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{-(-1)-\sqrt{401}}{2*2}=\frac{1-\sqrt{401}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{401}}{2*2}=\frac{1+\sqrt{401}}{4}
$