1/2x-10=2x+14

Solution for 1/2x-10=2x+14 equation:

1/2x-10=2x+14

We move all terms to the left:

1/2x-10-(2x+14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

1/2x-2x-14-10=0

We multiply all the terms by the denominator


-2x*2x-14*2x-10*2x+1=0

Wy multiply elements

-4x^2-28x-20x+1=0

We add all the numbers together, and all the variables

-4x^2-48x+1=0

a = -4; b = -48; c = +1;
Δ = b2-4ac
Δ = -482-4·(-4)·1
Δ = 2320
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:

$\sqrt{\Delta}=\sqrt{2320}=\sqrt{16*145}=\sqrt{16}*\sqrt{145}=4\sqrt{145}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-48)-4\sqrt{145}}{2*-4}=\frac{48-4\sqrt{145}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-48)+4\sqrt{145}}{2*-4}=\frac{48+4\sqrt{145}}{-8}
$