4x-1=3x2-4x-4

Solution for 4x-1=3x2-4x-4 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2+8x+3=0

a = -3; b = 8; c = +3;
Δ = b2-4ac
Δ = 82-4·(-3)·3
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8)-10}{2*-3}=\frac{-18}{-6}
=+3
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8)+10}{2*-3}=\frac{2}{-6}
=-1/3
$