x+1/2x=420

Solution for x+1/2x=420 equation:

x+1/2x=420

We move all terms to the left:

x+1/2x-(420)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


x*2x-420*2x+1=0

Wy multiply elements

2x^2-840x+1=0

a = 2; b = -840; c = +1;
Δ = b2-4ac
Δ = -8402-4·2·1
Δ = 705592
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:

$\sqrt{\Delta}=\sqrt{705592}=\sqrt{4*176398}=\sqrt{4}*\sqrt{176398}=2\sqrt{176398}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-2\sqrt{176398}}{2*2}=\frac{840-2\sqrt{176398}}{4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+2\sqrt{176398}}{2*2}=\frac{840+2\sqrt{176398}}{4}
$