(4x-1)(x-3)=3

Solution for (4x-1)(x-3)=3 equation:

(4x-1)(x-3)=3

We move all terms to the left:

(4x-1)(x-3)-(3)=0

We multiply parentheses ..

(+4x^2-12x-1x+3)-3=0

We get rid of parentheses

4x^2-12x-1x+3-3=0

We add all the numbers together, and all the variables

4x^2-13x=0

a = 4; b = -13; c = 0;
Δ = b2-4ac
Δ = -132-4·4·0
Δ = 169
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{169}=13$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-13)-13}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-13)+13}{2*4}=\frac{26}{8}
=3+1/4
$