1/2x+30=12+x

Solution for 1/2x+30=12+x equation:

1/2x+30=12+x

We move all terms to the left:

1/2x+30-(12+x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(x+12)+30=0

We get rid of parentheses

1/2x-x-12+30=0

We multiply all the terms by the denominator


-x*2x-12*2x+30*2x+1=0

Wy multiply elements

-2x^2-24x+60x+1=0

We add all the numbers together, and all the variables

-2x^2+36x+1=0

a = -2; b = 36; c = +1;
Δ = b2-4ac
Δ = 362-4·(-2)·1
Δ = 1304
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:

$\sqrt{\Delta}=\sqrt{1304}=\sqrt{4*326}=\sqrt{4}*\sqrt{326}=2\sqrt{326}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(36)-2\sqrt{326}}{2*-2}=\frac{-36-2\sqrt{326}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(36)+2\sqrt{326}}{2*-2}=\frac{-36+2\sqrt{326}}{-4}
$