(2x-1)(x+3)=12x-1

Solution for (2x-1)(x+3)=12x-1 equation:

(2x-1)(x+3)=12x-1

We move all terms to the left:

(2x-1)(x+3)-(12x-1)=0

We get rid of parentheses

(2x-1)(x+3)-12x+1=0

We multiply parentheses ..

(+2x^2+6x-1x-3)-12x+1=0

We get rid of parentheses

2x^2+6x-1x-12x-3+1=0

We add all the numbers together, and all the variables

2x^2-7x-2=0

a = 2; b = -7; c = -2;
Δ = b2-4ac
Δ = -72-4·2·(-2)
Δ = 65
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{65}}{2*2}=\frac{7-\sqrt{65}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{65}}{2*2}=\frac{7+\sqrt{65}}{4}
$