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

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

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

We move all terms to the left:

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


Domain of the equation: 4)(8x+4)!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

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

We multiply parentheses ..

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

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

Wy multiply elements

8x^2-32x*4+1=0

Wy multiply elements

8x^2-128x+1=0

a = 8; b = -128; c = +1;
Δ = b2-4ac
Δ = -1282-4·8·1
Δ = 16352
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:

$\sqrt{\Delta}=\sqrt{16352}=\sqrt{16*1022}=\sqrt{16}*\sqrt{1022}=4\sqrt{1022}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-128)-4\sqrt{1022}}{2*8}=\frac{128-4\sqrt{1022}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-128)+4\sqrt{1022}}{2*8}=\frac{128+4\sqrt{1022}}{16}
$