4x(2)-32=3x(2)-4x

Solution for 4x(2)-32=3x(2)-4x equation:

4x(2)-32=3x(2)-4x

We move all terms to the left:

4x(2)-32-(3x(2)-4x)=0

We add all the numbers together, and all the variables

-(+3x^2-4x)+4x2-32=0

We add all the numbers together, and all the variables

4x^2-(+3x^2-4x)-32=0

We get rid of parentheses

4x^2-3x^2+4x-32=0

We add all the numbers together, and all the variables

x^2+4x-32=0

a = 1; b = 4; c = -32;
Δ = b2-4ac
Δ = 42-4·1·(-32)
Δ = 144
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{144}=12$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(4)-12}{2*1}=\frac{-16}{2}
=-8
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(4)+12}{2*1}=\frac{8}{2}
=4
$