4x-1=3x^2-4

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

4x-1=3x^2-4

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -3; b = 4; c = +3;
Δ = b2-4ac
Δ = 42-4·(-3)·3
Δ = 52
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-2\sqrt{13}}{2*-3}=\frac{-4-2\sqrt{13}}{-6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+2\sqrt{13}}{2*-3}=\frac{-4+2\sqrt{13}}{-6}
$