1/2x+4=-2x+14

Solution for 1/2x+4=-2x+14 equation:

1/2x+4=-2x+14

We move all terms to the left:

1/2x+4-(-2x+14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x+2x-14+4=0

We multiply all the terms by the denominator


2x*2x-14*2x+4*2x+1=0

Wy multiply elements

4x^2-28x+8x+1=0

We add all the numbers together, and all the variables

4x^2-20x+1=0

a = 4; b = -20; c = +1;
Δ = b2-4ac
Δ = -202-4·4·1
Δ = 384
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:

$\sqrt{\Delta}=\sqrt{384}=\sqrt{64*6}=\sqrt{64}*\sqrt{6}=8\sqrt{6}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-20)-8\sqrt{6}}{2*4}=\frac{20-8\sqrt{6}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-20)+8\sqrt{6}}{2*4}=\frac{20+8\sqrt{6}}{8}
$