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

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

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

We move all terms to the left:

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


Domain of the equation: 2)(4x+4)!=0

x∈R


We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We get rid of parentheses

4x^2-6x*2*4+1=0

Wy multiply elements

4x^2-48x*4+1=0

Wy multiply elements

4x^2-192x+1=0

a = 4; b = -192; c = +1;
Δ = b2-4ac
Δ = -1922-4·4·1
Δ = 36848
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:

$\sqrt{\Delta}=\sqrt{36848}=\sqrt{784*47}=\sqrt{784}*\sqrt{47}=28\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-192)-28\sqrt{47}}{2*4}=\frac{192-28\sqrt{47}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-192)+28\sqrt{47}}{2*4}=\frac{192+28\sqrt{47}}{8}
$