1/2x-7x=6

Solution for 1/2x-7x=6 equation:

1/2x-7x=6

We move all terms to the left:

1/2x-7x-(6)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-7x+1/2x-6=0

We multiply all the terms by the denominator


-7x*2x-6*2x+1=0

Wy multiply elements

-14x^2-12x+1=0

a = -14; b = -12; c = +1;
Δ = b2-4ac
Δ = -122-4·(-14)·1
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-10\sqrt{2}}{2*-14}=\frac{12-10\sqrt{2}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+10\sqrt{2}}{2*-14}=\frac{12+10\sqrt{2}}{-28}
$