7/12x+1/2x=22+9/2x

Solution for 7/12x+1/2x=22+9/2x equation:

7/12x+1/2x=22+9/2x

We move all terms to the left:

7/12x+1/2x-(22+9/2x)=0


Domain of the equation: 12x!=0

x!=0/12

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

7/12x+1/2x-(9/2x+22)=0

We get rid of parentheses

7/12x+1/2x-9/2x-22=0

We calculate fractions


14x/24x^2+(-108x+1)/24x^2-22=0

We multiply all the terms by the denominator


14x+(-108x+1)-22*24x^2=0

Wy multiply elements

-528x^2+14x+(-108x+1)=0

We get rid of parentheses

-528x^2+14x-108x+1=0

We add all the numbers together, and all the variables

-528x^2-94x+1=0

a = -528; b = -94; c = +1;
Δ = b2-4ac
Δ = -942-4·(-528)·1
Δ = 10948
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:

$\sqrt{\Delta}=\sqrt{10948}=\sqrt{4*2737}=\sqrt{4}*\sqrt{2737}=2\sqrt{2737}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-94)-2\sqrt{2737}}{2*-528}=\frac{94-2\sqrt{2737}}{-1056}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-94)+2\sqrt{2737}}{2*-528}=\frac{94+2\sqrt{2737}}{-1056}
$