(1/2)(2x+4)-2x=-5

Solution for (1/2)(2x+4)-2x=-5 equation:

(1/2)(2x+4)-2x=-5

We move all terms to the left:

(1/2)(2x+4)-2x-(-5)=0


Domain of the equation: 2)(2x+4)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(2x+4)-2x-(-5)=0

We add all the numbers together, and all the variables

-2x+(+1/2)(2x+4)+5=0

We multiply parentheses ..

(+2x^2+1/2*4)-2x+5=0

We multiply all the terms by the denominator


(+2x^2+1-2x*2*4)+5*2*4)=0

We add all the numbers together, and all the variables

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

We get rid of parentheses

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

Wy multiply elements

2x^2-16x*4+1=0

Wy multiply elements

2x^2-64x+1=0

a = 2; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·2·1
Δ = 4088
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:

$\sqrt{\Delta}=\sqrt{4088}=\sqrt{4*1022}=\sqrt{4}*\sqrt{1022}=2\sqrt{1022}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-2\sqrt{1022}}{2*2}=\frac{64-2\sqrt{1022}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+2\sqrt{1022}}{2*2}=\frac{64+2\sqrt{1022}}{4}
$