4x(x-5)-(x-3)=3

Solution for 4x(x-5)-(x-3)=3 equation:

4x(x-5)-(x-3)=3

We move all terms to the left:

4x(x-5)-(x-3)-(3)=0

We multiply parentheses

4x^2-20x-(x-3)-3=0

We get rid of parentheses

4x^2-20x-x+3-3=0

We add all the numbers together, and all the variables

4x^2-21x=0

a = 4; b = -21; c = 0;
Δ = b2-4ac
Δ = -212-4·4·0
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-21}{2*4}=\frac{0}{8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+21}{2*4}=\frac{42}{8}
=5+1/4
$