x+7=1/2x+9

Solution for x+7=1/2x+9 equation:

x+7=1/2x+9

We move all terms to the left:

x+7-(1/2x+9)=0


Domain of the equation: 2x+9)!=0

x∈R


We get rid of parentheses

x-1/2x-9+7=0

We multiply all the terms by the denominator


x*2x-9*2x+7*2x-1=0

Wy multiply elements

2x^2-18x+14x-1=0

We add all the numbers together, and all the variables

2x^2-4x-1=0

a = 2; b = -4; c = -1;
Δ = b2-4ac
Δ = -42-4·2·(-1)
Δ = 24
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:

$\sqrt{\Delta}=\sqrt{24}=\sqrt{4*6}=\sqrt{4}*\sqrt{6}=2\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{6}}{2*2}=\frac{4-2\sqrt{6}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{6}}{2*2}=\frac{4+2\sqrt{6}}{4}
$