4(x+1)=3(x2)

Solution for 4(x+1)=3(x2) equation:

4(x+1)=3(x2)

We move all terms to the left:

4(x+1)-(3(x2))=0

determiningTheFunctionDomain
4(x+1)-3x2=0

We add all the numbers together, and all the variables

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

We multiply parentheses

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

a = -3; b = 4; c = +4;
Δ = b2-4ac
Δ = 42-4·(-3)·4
Δ = 64
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{64}=8$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-8}{2*-3}=\frac{-12}{-6}
=+2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+8}{2*-3}=\frac{4}{-6}
=-2/3
$