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

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

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

We move all terms to the left:

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


Domain of the equation: 2)x!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

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

We multiply parentheses

x^2-(4x+4)-6=0

We get rid of parentheses

x^2-4x-4-6=0

We add all the numbers together, and all the variables

x^2-4x-10=0

a = 1; b = -4; c = -10;
Δ = b2-4ac
Δ = -42-4·1·(-10)
Δ = 56
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:

$\sqrt{\Delta}=\sqrt{56}=\sqrt{4*14}=\sqrt{4}*\sqrt{14}=2\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{14}}{2*1}=\frac{4-2\sqrt{14}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{14}}{2*1}=\frac{4+2\sqrt{14}}{2}
$