-1/2x+6.5=2x-6.5

Solution for -1/2x+6.5=2x-6.5 equation:

-1/2x+6.5=2x-6.5

We move all terms to the left:

-1/2x+6.5-(2x-6.5)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We get rid of parentheses

-1/2x-2x+6.5+6.5=0

We multiply all the terms by the denominator


-2x*2x+(6.5)*2x+(6.5)*2x-1=0

We multiply parentheses

-2x*2x+13x+13x-1=0

Wy multiply elements

-4x^2+13x+13x-1=0

We add all the numbers together, and all the variables

-4x^2+26x-1=0

a = -4; b = 26; c = -1;
Δ = b2-4ac
Δ = 262-4·(-4)·(-1)
Δ = 660
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:

$\sqrt{\Delta}=\sqrt{660}=\sqrt{4*165}=\sqrt{4}*\sqrt{165}=2\sqrt{165}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-2\sqrt{165}}{2*-4}=\frac{-26-2\sqrt{165}}{-8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+2\sqrt{165}}{2*-4}=\frac{-26+2\sqrt{165}}{-8}
$