1/2x+3=-x+9

Solution for 1/2x+3=-x+9 equation:

1/2x+3=-x+9

We move all terms to the left:

1/2x+3-(-x+9)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

1/2x-(-1x+9)+3=0

We get rid of parentheses

1/2x+1x-9+3=0

We multiply all the terms by the denominator


1x*2x-9*2x+3*2x+1=0

Wy multiply elements

2x^2-18x+6x+1=0

We add all the numbers together, and all the variables

2x^2-12x+1=0

a = 2; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·2·1
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-2\sqrt{34}}{2*2}=\frac{12-2\sqrt{34}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+2\sqrt{34}}{2*2}=\frac{12+2\sqrt{34}}{4}
$