4x^2-1=3x+2

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

4x^2-1=3x+2

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

4x^2-3x-3=0

a = 4; b = -3; c = -3;
Δ = b2-4ac
Δ = -32-4·4·(-3)
Δ = 57
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{-(-3)-\sqrt{57}}{2*4}=\frac{3-\sqrt{57}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+\sqrt{57}}{2*4}=\frac{3+\sqrt{57}}{8}
$