(2x-1)(x-3)=6

Solution for (2x-1)(x-3)=6 equation:

(2x-1)(x-3)=6

We move all terms to the left:

(2x-1)(x-3)-(6)=0

We multiply parentheses ..

(+2x^2-6x-1x+3)-6=0

We get rid of parentheses

2x^2-6x-1x+3-6=0

We add all the numbers together, and all the variables

2x^2-7x-3=0

a = 2; b = -7; c = -3;
Δ = b2-4ac
Δ = -72-4·2·(-3)
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{-(-7)-\sqrt{73}}{2*2}=\frac{7-\sqrt{73}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{73}}{2*2}=\frac{7+\sqrt{73}}{4}
$