30+x=22+1/2x

Solution for 30+x=22+1/2x equation:

30+x=22+1/2x

We move all terms to the left:

30+x-(22+1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

x-(1/2x+22)+30=0

We get rid of parentheses

x-1/2x-22+30=0

We multiply all the terms by the denominator


x*2x-22*2x+30*2x-1=0

Wy multiply elements

2x^2-44x+60x-1=0

We add all the numbers together, and all the variables

2x^2+16x-1=0

a = 2; b = 16; c = -1;
Δ = b2-4ac
Δ = 162-4·2·(-1)
Δ = 264
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:

$\sqrt{\Delta}=\sqrt{264}=\sqrt{4*66}=\sqrt{4}*\sqrt{66}=2\sqrt{66}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{66}}{2*2}=\frac{-16-2\sqrt{66}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{66}}{2*2}=\frac{-16+2\sqrt{66}}{4}
$