(x-3)(2x+1)=22

Solution for (x-3)(2x+1)=22 equation:

(x-3)(2x+1)=22

We move all terms to the left:

(x-3)(2x+1)-(22)=0

We multiply parentheses ..

(+2x^2+x-6x-3)-22=0

We get rid of parentheses

2x^2+x-6x-3-22=0

We add all the numbers together, and all the variables

2x^2-5x-25=0

a = 2; b = -5; c = -25;
Δ = b2-4ac
Δ = -52-4·2·(-25)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-15}{2*2}=\frac{-10}{4}
=-2+1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+15}{2*2}=\frac{20}{4}
=5
$