3x+5=21-1/2x

Solution for 3x+5=21-1/2x equation:

3x+5=21-1/2x

We move all terms to the left:

3x+5-(21-1/2x)=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+21)+5=0

We get rid of parentheses

3x+1/2x-21+5=0

We multiply all the terms by the denominator


3x*2x-21*2x+5*2x+1=0

Wy multiply elements

6x^2-42x+10x+1=0

We add all the numbers together, and all the variables

6x^2-32x+1=0

a = 6; b = -32; c = +1;
Δ = b2-4ac
Δ = -322-4·6·1
Δ = 1000
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:

$\sqrt{\Delta}=\sqrt{1000}=\sqrt{100*10}=\sqrt{100}*\sqrt{10}=10\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-32)-10\sqrt{10}}{2*6}=\frac{32-10\sqrt{10}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-32)+10\sqrt{10}}{2*6}=\frac{32+10\sqrt{10}}{12}
$