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

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

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

We move all terms to the left:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

2x^2-5x-6=0

a = 2; b = -5; c = -6;
Δ = b2-4ac
Δ = -52-4·2·(-6)
Δ = 73
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{-(-5)-\sqrt{73}}{2*2}=\frac{5-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{73}}{2*2}=\frac{5+\sqrt{73}}{4}
$