1/2x-7.x=18

Solution for 1/2x-7.x=18 equation:

1/2x-7.x=18

We move all terms to the left:

1/2x-7.x-(18)=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-18=0

We multiply all the terms by the denominator


-7x*2x-18*2x+1=0

Wy multiply elements

-14x^2-36x+1=0

a = -14; b = -36; c = +1;
Δ = b2-4ac
Δ = -362-4·(-14)·1
Δ = 1352
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:

$\sqrt{\Delta}=\sqrt{1352}=\sqrt{676*2}=\sqrt{676}*\sqrt{2}=26\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-36)-26\sqrt{2}}{2*-14}=\frac{36-26\sqrt{2}}{-28}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-36)+26\sqrt{2}}{2*-14}=\frac{36+26\sqrt{2}}{-28}
$