-2x+6=-1/2x+3

Solution for -2x+6=-1/2x+3 equation:

-2x+6=-1/2x+3

We move all terms to the left:

-2x+6-(-1/2x+3)=0


Domain of the equation: 2x+3)!=0

x∈R


We get rid of parentheses

-2x+1/2x-3+6=0

We multiply all the terms by the denominator


-2x*2x-3*2x+6*2x+1=0

Wy multiply elements

-4x^2-6x+12x+1=0

We add all the numbers together, and all the variables

-4x^2+6x+1=0

a = -4; b = 6; c = +1;
Δ = b2-4ac
Δ = 62-4·(-4)·1
Δ = 52
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:

$\sqrt{\Delta}=\sqrt{52}=\sqrt{4*13}=\sqrt{4}*\sqrt{13}=2\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6)-2\sqrt{13}}{2*-4}=\frac{-6-2\sqrt{13}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6)+2\sqrt{13}}{2*-4}=\frac{-6+2\sqrt{13}}{-8}
$