(1/2)(8x-4)=3x

Solution for (1/2)(8x-4)=3x equation:

(1/2)(8x-4)=3x

We move all terms to the left:

(1/2)(8x-4)-(3x)=0


Domain of the equation: 2)(8x-4)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(8x-4)-3x=0

We add all the numbers together, and all the variables

-3x+(+1/2)(8x-4)=0

We multiply parentheses ..

(+8x^2+1/2*-4)-3x=0

We multiply all the terms by the denominator


(+8x^2+1-3x*2*-4)=0

We get rid of parentheses

8x^2-3x*2*+1-4=0

We add all the numbers together, and all the variables

8x^2-3x*2*-3=0

Wy multiply elements

8x^2-6x^2-3=0

We add all the numbers together, and all the variables

2x^2-3=0

a = 2; b = 0; c = -3;
Δ = b2-4ac
Δ = 02-4·2·(-3)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{6}}{2*2}=\frac{0-2\sqrt{6}}{4}
=-\frac{2\sqrt{6}}{4}
=-\frac{\sqrt{6}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{6}}{2*2}=\frac{0+2\sqrt{6}}{4}
=\frac{2\sqrt{6}}{4}
=\frac{\sqrt{6}}{2}
$