/2x-5=x+3+x-8*

Solution for /2x-5=x+3+x-8* equation:

/2x-5=x+3+x-8*

We move all terms to the left:

/2x-5-(x+3+x-8*)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

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

We get rid of parentheses

/2x-2x-5=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

-2x*2x-5*2x=0

Wy multiply elements

-4x^2-10x=0

a = -4; b = -10; c = 0;
Δ = b2-4ac
Δ = -102-4·(-4)·0
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-10}{2*-4}=\frac{0}{-8}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+10}{2*-4}=\frac{20}{-8}
=-2+1/2
$