X+1/2x=70

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

X+1/2X=70

We move all terms to the left:

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


Domain of the equation: 2X!=0

X!=0/2

X!=0

X∈R


We multiply all the terms by the denominator


X*2X-70*2X+1=0

Wy multiply elements

2X^2-140X+1=0

a = 2; b = -140; c = +1;
Δ = b2-4ac
Δ = -1402-4·2·1
Δ = 19592
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:

$\sqrt{\Delta}=\sqrt{19592}=\sqrt{4*4898}=\sqrt{4}*\sqrt{4898}=2\sqrt{4898}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-140)-2\sqrt{4898}}{2*2}=\frac{140-2\sqrt{4898}}{4}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-140)+2\sqrt{4898}}{2*2}=\frac{140+2\sqrt{4898}}{4}
$