7/2x+6=x+12

Solution for 7/2x+6=x+12 equation:

7/2x+6=x+12

We move all terms to the left:

7/2x+6-(x+12)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

7/2x-x-12+6=0

We multiply all the terms by the denominator


-x*2x-12*2x+6*2x+7=0

Wy multiply elements

-2x^2-24x+12x+7=0

We add all the numbers together, and all the variables

-2x^2-12x+7=0

a = -2; b = -12; c = +7;
Δ = b2-4ac
Δ = -122-4·(-2)·7
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10\sqrt{2}}{2*-2}=\frac{12-10\sqrt{2}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10\sqrt{2}}{2*-2}=\frac{12+10\sqrt{2}}{-4}
$