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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-7x-1=0

a = 4; b = -7; c = -1;
Δ = b2-4ac
Δ = -72-4·4·(-1)
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*4}=\frac{7-\sqrt{65}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{65}}{2*4}=\frac{7+\sqrt{65}}{8}
$