1/2x=10-3x

Solution for 1/2x=10-3x equation:

1/2x=10-3x

We move all terms to the left:

1/2x-(10-3x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-3x+10)=0

We get rid of parentheses

1/2x+3x-10=0

We multiply all the terms by the denominator


3x*2x-10*2x+1=0

Wy multiply elements

6x^2-20x+1=0

a = 6; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·6·1
Δ = 376
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:

$\sqrt{\Delta}=\sqrt{376}=\sqrt{4*94}=\sqrt{4}*\sqrt{94}=2\sqrt{94}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-2\sqrt{94}}{2*6}=\frac{20-2\sqrt{94}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+2\sqrt{94}}{2*6}=\frac{20+2\sqrt{94}}{12}
$