(1/2)(8-6x)=x

Solution for (1/2)(8-6x)=x equation:

(1/2)(8-6x)=x

We move all terms to the left:

(1/2)(8-6x)-(x)=0


Domain of the equation: 2)(8-6x)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(-6x+8)-x=0

We add all the numbers together, and all the variables

-1x+(+1/2)(-6x+8)=0

We multiply parentheses ..

(-6x^2+1/2*8)-1x=0

We multiply all the terms by the denominator


(-6x^2+1-1x*2*8)=0

We get rid of parentheses

-6x^2-1x*2*8+1=0

Wy multiply elements

-6x^2-16x*8+1=0

Wy multiply elements

-6x^2-128x+1=0

a = -6; b = -128; c = +1;
Δ = b2-4ac
Δ = -1282-4·(-6)·1
Δ = 16408
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:

$\sqrt{\Delta}=\sqrt{16408}=\sqrt{4*4102}=\sqrt{4}*\sqrt{4102}=2\sqrt{4102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-2\sqrt{4102}}{2*-6}=\frac{128-2\sqrt{4102}}{-12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+2\sqrt{4102}}{2*-6}=\frac{128+2\sqrt{4102}}{-12}
$