2(x-1)+(1/2)(4x+6)=5

Solution for 2(x-1)+(1/2)(4x+6)=5 equation:

2(x-1)+(1/2)(4x+6)=5

We move all terms to the left:

2(x-1)+(1/2)(4x+6)-(5)=0


Domain of the equation: 2)(4x+6)!=0

x∈R


We add all the numbers together, and all the variables

2(x-1)+(+1/2)(4x+6)-5=0

We multiply parentheses

2x+(+1/2)(4x+6)-2-5=0

We multiply parentheses ..

(+4x^2+1/2*6)+2x-2-5=0

We multiply all the terms by the denominator


(+4x^2+1+2x*2*6)-2*2*6)-5*2*6)=0

We add all the numbers together, and all the variables

(+4x^2+1+2x*2*6)=0

We get rid of parentheses

4x^2+2x*2*6+1=0

Wy multiply elements

4x^2+24x*6+1=0

Wy multiply elements

4x^2+144x+1=0

a = 4; b = 144; c = +1;
Δ = b2-4ac
Δ = 1442-4·4·1
Δ = 20720
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:

$\sqrt{\Delta}=\sqrt{20720}=\sqrt{16*1295}=\sqrt{16}*\sqrt{1295}=4\sqrt{1295}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(144)-4\sqrt{1295}}{2*4}=\frac{-144-4\sqrt{1295}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(144)+4\sqrt{1295}}{2*4}=\frac{-144+4\sqrt{1295}}{8}
$