(3-4)^2+2x=4(1/2x-6)

Solution for (3-4)^2+2x=4(1/2x-6) equation:

(3-4)^2+2x=4(1/2x-6)

We move all terms to the left:

(3-4)^2+2x-(4(1/2x-6))=0


Domain of the equation: 2x-6))!=0

x∈R


We add all the numbers together, and all the variables

2x-(4(1/2x-6))+(-1)^2=0

We add all the numbers together, and all the variables

2x-(4(1/2x-6))+1=0

We multiply all the terms by the denominator


2x*2x+1*2x-6))-(4(1-6))=0

We add all the numbers together, and all the variables

2x*2x+1*2x-6))-(4(-5))=0

We add all the numbers together, and all the variables

2x*2x+1*2x=0

Wy multiply elements

4x^2+2x=0

a = 4; b = 2; c = 0;
Δ = b2-4ac
Δ = 22-4·4·0
Δ = 4
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4}=2$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(2)-2}{2*4}=\frac{-4}{8}
=-1/2
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(2)+2}{2*4}=\frac{0}{8}
=0
$