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

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

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

We move all terms to the left:

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


Domain of the equation: 2x+5)!=0

x∈R


We get rid of parentheses

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

We multiply all the terms by the denominator


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

Wy multiply elements

6x^2-10x-10x+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}
$