1/2x+32=6x+4.5

Solution for 1/2x+32=6x+4.5 equation:

1/2x+32=6x+4.5

We move all terms to the left:

1/2x+32-(6x+4.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-6x-4.5+32=0

We multiply all the terms by the denominator


-6x*2x-(4.5)*2x+32*2x+1=0

We multiply parentheses

-6x*2x-9x+32*2x+1=0

Wy multiply elements

-12x^2-9x+64x+1=0

We add all the numbers together, and all the variables

-12x^2+55x+1=0

a = -12; b = 55; c = +1;
Δ = b2-4ac
Δ = 552-4·(-12)·1
Δ = 3073
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(55)-\sqrt{3073}}{2*-12}=\frac{-55-\sqrt{3073}}{-24}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(55)+\sqrt{3073}}{2*-12}=\frac{-55+\sqrt{3073}}{-24}
$