(-1/2x+6)-(4x-4)=0

Solution for (-1/2x+6)-(4x-4)=0 equation:

(-1/2x+6)-(4x-4)=0


Domain of the equation: 2x+6)!=0

x∈R


We get rid of parentheses

-1/2x-4x+6+4=0

We multiply all the terms by the denominator


-4x*2x+6*2x+4*2x-1=0

Wy multiply elements

-8x^2+12x+8x-1=0

We add all the numbers together, and all the variables

-8x^2+20x-1=0

a = -8; b = 20; c = -1;
Δ = b2-4ac
Δ = 202-4·(-8)·(-1)
Δ = 368
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:

$\sqrt{\Delta}=\sqrt{368}=\sqrt{16*23}=\sqrt{16}*\sqrt{23}=4\sqrt{23}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{23}}{2*-8}=\frac{-20-4\sqrt{23}}{-16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{23}}{2*-8}=\frac{-20+4\sqrt{23}}{-16}
$