-(1/2)x+3=x-7

Solution for -(1/2)x+3=x-7 equation:

-(1/2)x+3=x-7

We move all terms to the left:

-(1/2)x+3-(x-7)=0


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-(+1/2)x-(x-7)+3=0

We multiply parentheses

-x^2-(x-7)+3=0

We get rid of parentheses

-x^2-x+7+3=0

We add all the numbers together, and all the variables

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

a = -1; b = -1; c = +10;
Δ = b2-4ac
Δ = -12-4·(-1)·10
Δ = 41
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-\sqrt{41}}{2*-1}=\frac{1-\sqrt{41}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+\sqrt{41}}{2*-1}=\frac{1+\sqrt{41}}{-2}
$