(1/2)(12x+8)-(4x+4)=50

Solution for (1/2)(12x+8)-(4x+4)=50 equation:

(1/2)(12x+8)-(4x+4)=50

We move all terms to the left:

(1/2)(12x+8)-(4x+4)-(50)=0


Domain of the equation: 2)(12x+8)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(12x+8)-(4x+4)-50=0

We get rid of parentheses

(+1/2)(12x+8)-4x-4-50=0

We multiply parentheses ..

(+12x^2+1/2*8)-4x-4-50=0

We multiply all the terms by the denominator


(+12x^2+1-4x*2*8)-4*2*8)-50*2*8)=0

We add all the numbers together, and all the variables

(+12x^2+1-4x*2*8)=0

We get rid of parentheses

12x^2-4x*2*8+1=0

Wy multiply elements

12x^2-64x*8+1=0

Wy multiply elements

12x^2-512x+1=0

a = 12; b = -512; c = +1;
Δ = b2-4ac
Δ = -5122-4·12·1
Δ = 262096
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:

$\sqrt{\Delta}=\sqrt{262096}=\sqrt{16*16381}=\sqrt{16}*\sqrt{16381}=4\sqrt{16381}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-512)-4\sqrt{16381}}{2*12}=\frac{512-4\sqrt{16381}}{24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-512)+4\sqrt{16381}}{2*12}=\frac{512+4\sqrt{16381}}{24}
$