x+3.5=1/2x+12

Solution for x+3.5=1/2x+12 equation:

x+3.5=1/2x+12

We move all terms to the left:

x+3.5-(1/2x+12)=0


Domain of the equation: 2x+12)!=0

x∈R


We get rid of parentheses

x-1/2x-12+3.5=0

We multiply all the terms by the denominator


x*2x-12*2x+(3.5)*2x-1=0

We multiply parentheses

x*2x-12*2x+7x-1=0

Wy multiply elements

2x^2-24x+7x-1=0

We add all the numbers together, and all the variables

2x^2-17x-1=0

a = 2; b = -17; c = -1;
Δ = b2-4ac
Δ = -172-4·2·(-1)
Δ = 297
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:

$\sqrt{\Delta}=\sqrt{297}=\sqrt{9*33}=\sqrt{9}*\sqrt{33}=3\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-17)-3\sqrt{33}}{2*2}=\frac{17-3\sqrt{33}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-17)+3\sqrt{33}}{2*2}=\frac{17+3\sqrt{33}}{4}
$