2x=1/2x+70

Solution for 2x=1/2x+70 equation:

2x=1/2x+70

We move all terms to the left:

2x-(1/2x+70)=0


Domain of the equation: 2x+70)!=0

x∈R


We get rid of parentheses

2x-1/2x-70=0

We multiply all the terms by the denominator


2x*2x-70*2x-1=0

Wy multiply elements

4x^2-140x-1=0

a = 4; b = -140; c = -1;
Δ = b2-4ac
Δ = -1402-4·4·(-1)
Δ = 19616
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:

$\sqrt{\Delta}=\sqrt{19616}=\sqrt{16*1226}=\sqrt{16}*\sqrt{1226}=4\sqrt{1226}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-4\sqrt{1226}}{2*4}=\frac{140-4\sqrt{1226}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+4\sqrt{1226}}{2*4}=\frac{140+4\sqrt{1226}}{8}
$