15-3x=5+1/2x

Solution for 15-3x=5+1/2x equation:

15-3x=5+1/2x

We move all terms to the left:

15-3x-(5+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+5)+15=0

We get rid of parentheses

-3x-1/2x-5+15=0

We multiply all the terms by the denominator


-3x*2x-5*2x+15*2x-1=0

Wy multiply elements

-6x^2-10x+30x-1=0

We add all the numbers together, and all the variables

-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}
$