3x=1/2x+22.5

Solution for 3x=1/2x+22.5 equation:

3x=1/2x+22.5

We move all terms to the left:

3x-(1/2x+22.5)=0


Domain of the equation: 2x+22.5)!=0

x∈R


We get rid of parentheses

3x-1/2x-22.5=0

We multiply all the terms by the denominator


3x*2x-(22.5)*2x-1=0

We multiply parentheses

3x*2x-45x-1=0

Wy multiply elements

6x^2-45x-1=0

a = 6; b = -45; c = -1;
Δ = b2-4ac
Δ = -452-4·6·(-1)
Δ = 2049
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{-(-45)-\sqrt{2049}}{2*6}=\frac{45-\sqrt{2049}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2049}}{2*6}=\frac{45+\sqrt{2049}}{12}
$