-1/2x+3=2x-14

Solution for -1/2x+3=2x-14 equation:

-1/2x+3=2x-14

We move all terms to the left:

-1/2x+3-(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+3=0

We multiply all the terms by the denominator


-2x*2x+14*2x+3*2x-1=0

Wy multiply elements

-4x^2+28x+6x-1=0

We add all the numbers together, and all the variables

-4x^2+34x-1=0

a = -4; b = 34; c = -1;
Δ = b2-4ac
Δ = 342-4·(-4)·(-1)
Δ = 1140
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:

$\sqrt{\Delta}=\sqrt{1140}=\sqrt{4*285}=\sqrt{4}*\sqrt{285}=2\sqrt{285}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(34)-2\sqrt{285}}{2*-4}=\frac{-34-2\sqrt{285}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(34)+2\sqrt{285}}{2*-4}=\frac{-34+2\sqrt{285}}{-8}
$