3x+5=30-1/2x

Solution for 3x+5=30-1/2x equation:

3x+5=30-1/2x

We move all terms to the left:

3x+5-(30-1/2x)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

3x-(-1/2x+30)+5=0

We get rid of parentheses

3x+1/2x-30+5=0

We multiply all the terms by the denominator


3x*2x-30*2x+5*2x+1=0

Wy multiply elements

6x^2-60x+10x+1=0

We add all the numbers together, and all the variables

6x^2-50x+1=0

a = 6; b = -50; c = +1;
Δ = b2-4ac
Δ = -502-4·6·1
Δ = 2476
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:

$\sqrt{\Delta}=\sqrt{2476}=\sqrt{4*619}=\sqrt{4}*\sqrt{619}=2\sqrt{619}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{619}}{2*6}=\frac{50-2\sqrt{619}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{619}}{2*6}=\frac{50+2\sqrt{619}}{12}
$