30x=22-1/2x

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

30x=22-1/2x

We move all terms to the left:

30x-(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

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

We get rid of parentheses

30x+1/2x-22=0

We multiply all the terms by the denominator


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

Wy multiply elements

60x^2-44x+1=0

a = 60; b = -44; c = +1;
Δ = b2-4ac
Δ = -442-4·60·1
Δ = 1696
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:

$\sqrt{\Delta}=\sqrt{1696}=\sqrt{16*106}=\sqrt{16}*\sqrt{106}=4\sqrt{106}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-4\sqrt{106}}{2*60}=\frac{44-4\sqrt{106}}{120}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+4\sqrt{106}}{2*60}=\frac{44+4\sqrt{106}}{120}
$