(1/2)(x+29)=x+19

Solution for (1/2)(x+29)=x+19 equation:

(1/2)(x+29)=x+19

We move all terms to the left:

(1/2)(x+29)-(x+19)=0


Domain of the equation: 2)(x+29)!=0

x∈R


We add all the numbers together, and all the variables

(+1/2)(x+29)-(x+19)=0

We get rid of parentheses

(+1/2)(x+29)-x-19=0

We multiply parentheses ..

(+x^2+1/2*29)-x-19=0

We multiply all the terms by the denominator


(+x^2+1-x*2*29)-19*2*29)=0

We add all the numbers together, and all the variables

(+x^2+1-x*2*29)=0

We get rid of parentheses

x^2-x*2*29+1=0

Wy multiply elements

x^2-58x*2+1=0

Wy multiply elements

x^2-116x+1=0

a = 1; b = -116; c = +1;
Δ = b2-4ac
Δ = -1162-4·1·1
Δ = 13452
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:

$\sqrt{\Delta}=\sqrt{13452}=\sqrt{4*3363}=\sqrt{4}*\sqrt{3363}=2\sqrt{3363}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-116)-2\sqrt{3363}}{2*1}=\frac{116-2\sqrt{3363}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-116)+2\sqrt{3363}}{2*1}=\frac{116+2\sqrt{3363}}{2}
$