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

Solution for 4x^2-4x-1=x+3 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-5x-4=0

a = 4; b = -5; c = -4;
Δ = b2-4ac
Δ = -52-4·4·(-4)
Δ = 89
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{-(-5)-\sqrt{89}}{2*4}=\frac{5-\sqrt{89}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{89}}{2*4}=\frac{5+\sqrt{89}}{8}
$