32=1/2x+2x+12

Solution for 32=1/2x+2x+12 equation:

32=1/2x+2x+12

We move all terms to the left:

32-(1/2x+2x+12)=0


Domain of the equation: 2x+2x+12)!=0

x∈R


We add all the numbers together, and all the variables

-(2x+1/2x+12)+32=0

We get rid of parentheses

-2x-1/2x-12+32=0

We multiply all the terms by the denominator


-2x*2x-12*2x+32*2x-1=0

Wy multiply elements

-4x^2-24x+64x-1=0

We add all the numbers together, and all the variables

-4x^2+40x-1=0

a = -4; b = 40; c = -1;
Δ = b2-4ac
Δ = 402-4·(-4)·(-1)
Δ = 1584
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:

$\sqrt{\Delta}=\sqrt{1584}=\sqrt{144*11}=\sqrt{144}*\sqrt{11}=12\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-12\sqrt{11}}{2*-4}=\frac{-40-12\sqrt{11}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+12\sqrt{11}}{2*-4}=\frac{-40+12\sqrt{11}}{-8}
$