1/2x+6=x-14

Solution for 1/2x+6=x-14 equation:

1/2x+6=x-14

We move all terms to the left:

1/2x+6-(x-14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-x+14+6=0

We multiply all the terms by the denominator


-x*2x+14*2x+6*2x+1=0

Wy multiply elements

-2x^2+28x+12x+1=0

We add all the numbers together, and all the variables

-2x^2+40x+1=0

a = -2; b = 40; c = +1;
Δ = b2-4ac
Δ = 402-4·(-2)·1
Δ = 1608
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:

$\sqrt{\Delta}=\sqrt{1608}=\sqrt{4*402}=\sqrt{4}*\sqrt{402}=2\sqrt{402}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-2\sqrt{402}}{2*-2}=\frac{-40-2\sqrt{402}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+2\sqrt{402}}{2*-2}=\frac{-40+2\sqrt{402}}{-4}
$