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

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

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

We move all terms to the left:

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


Domain of the equation: 2)(3x-8)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

3x^2-x*2*-7=0

Wy multiply elements

3x^2-2x^2-7=0

We add all the numbers together, and all the variables

x^2-7=0

a = 1; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·1·(-7)
Δ = 28
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:

$\sqrt{\Delta}=\sqrt{28}=\sqrt{4*7}=\sqrt{4}*\sqrt{7}=2\sqrt{7}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{7}}{2*1}=\frac{0-2\sqrt{7}}{2}
=-\frac{2\sqrt{7}}{2}
=-\sqrt{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{7}}{2*1}=\frac{0+2\sqrt{7}}{2}
=\frac{2\sqrt{7}}{2}
=\sqrt{7}
$