1/2x-710=x

Solution for 1/2x-710=x equation:

1/2x-710=x

We move all terms to the left:

1/2x-710-(x)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We add all the numbers together, and all the variables

-1x+1/2x-710=0

We multiply all the terms by the denominator


-1x*2x-710*2x+1=0

Wy multiply elements

-2x^2-1420x+1=0

a = -2; b = -1420; c = +1;
Δ = b2-4ac
Δ = -14202-4·(-2)·1
Δ = 2016408
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:

$\sqrt{\Delta}=\sqrt{2016408}=\sqrt{4*504102}=\sqrt{4}*\sqrt{504102}=2\sqrt{504102}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1420)-2\sqrt{504102}}{2*-2}=\frac{1420-2\sqrt{504102}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1420)+2\sqrt{504102}}{2*-2}=\frac{1420+2\sqrt{504102}}{-4}
$