/2x-2=-x+10

Solution for /2x-2=-x+10 equation:

/2x-2=-x+10

We move all terms to the left:

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

We get rid of parentheses

/2x+1x-10-2=0

We multiply all the terms by the denominator


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

We add all the numbers together, and all the variables

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

Wy multiply elements

2x^2-20x-4x=0

We add all the numbers together, and all the variables

2x^2-24x=0

a = 2; b = -24; c = 0;
Δ = b2-4ac
Δ = -242-4·2·0
Δ = 576
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{576}=24$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-24}{2*2}=\frac{0}{4}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+24}{2*2}=\frac{48}{4}
=12
$