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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

Wy multiply elements

3x^2-32x*8+1=0

Wy multiply elements

3x^2-256x+1=0

a = 3; b = -256; c = +1;
Δ = b2-4ac
Δ = -2562-4·3·1
Δ = 65524
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:

$\sqrt{\Delta}=\sqrt{65524}=\sqrt{4*16381}=\sqrt{4}*\sqrt{16381}=2\sqrt{16381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-256)-2\sqrt{16381}}{2*3}=\frac{256-2\sqrt{16381}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-256)+2\sqrt{16381}}{2*3}=\frac{256+2\sqrt{16381}}{6}
$