-1/2x+2=7x-14

Solution for -1/2x+2=7x-14 equation:

-1/2x+2=7x-14

We move all terms to the left:

-1/2x+2-(7x-14)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-7x+14+2=0

We multiply all the terms by the denominator


-7x*2x+14*2x+2*2x-1=0

Wy multiply elements

-14x^2+28x+4x-1=0

We add all the numbers together, and all the variables

-14x^2+32x-1=0

a = -14; b = 32; c = -1;
Δ = b2-4ac
Δ = 322-4·(-14)·(-1)
Δ = 968
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:

$\sqrt{\Delta}=\sqrt{968}=\sqrt{484*2}=\sqrt{484}*\sqrt{2}=22\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(32)-22\sqrt{2}}{2*-14}=\frac{-32-22\sqrt{2}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(32)+22\sqrt{2}}{2*-14}=\frac{-32+22\sqrt{2}}{-28}
$