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

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

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

We move all terms to the left:

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


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

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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


We calculate terms in parentheses: -((+x^2+1+4x*2*-8)), so:

(+x^2+1+4x*2*-8)

We get rid of parentheses

x^2+4x*2*+1-8

We add all the numbers together, and all the variables

x^2+4x*2*-7

Wy multiply elements

x^2+8x^2-7

We add all the numbers together, and all the variables

9x^2-7

Back to the equation:

-(9x^2-7)


We add all the numbers together, and all the variables

-(9x^2-7)=0

We get rid of parentheses

-9x^2+7=0

a = -9; b = 0; c = +7;
Δ = b2-4ac
Δ = 02-4·(-9)·7
Δ = 252
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:

$\sqrt{\Delta}=\sqrt{252}=\sqrt{36*7}=\sqrt{36}*\sqrt{7}=6\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-6\sqrt{7}}{2*-9}=\frac{0-6\sqrt{7}}{-18}
=-\frac{6\sqrt{7}}{-18}
=-\frac{\sqrt{7}}{-3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+6\sqrt{7}}{2*-9}=\frac{0+6\sqrt{7}}{-18}
=\frac{6\sqrt{7}}{-18}
=\frac{\sqrt{7}}{-3}
$