2x+3=1/2x+30

Solution for 2x+3=1/2x+30 equation:

2x+3=1/2x+30

We move all terms to the left:

2x+3-(1/2x+30)=0


Domain of the equation: 2x+30)!=0

x∈R


We get rid of parentheses

2x-1/2x-30+3=0

We multiply all the terms by the denominator


2x*2x-30*2x+3*2x-1=0

Wy multiply elements

4x^2-60x+6x-1=0

We add all the numbers together, and all the variables

4x^2-54x-1=0

a = 4; b = -54; c = -1;
Δ = b2-4ac
Δ = -542-4·4·(-1)
Δ = 2932
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:

$\sqrt{\Delta}=\sqrt{2932}=\sqrt{4*733}=\sqrt{4}*\sqrt{733}=2\sqrt{733}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-54)-2\sqrt{733}}{2*4}=\frac{54-2\sqrt{733}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-54)+2\sqrt{733}}{2*4}=\frac{54+2\sqrt{733}}{8}
$