2x+3/2x=420

Solution for 2x+3/2x=420 equation:

2x+3/2x=420

We move all terms to the left:

2x+3/2x-(420)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-420*2x+3=0

Wy multiply elements

4x^2-840x+3=0

a = 4; b = -840; c = +3;
Δ = b2-4ac
Δ = -8402-4·4·3
Δ = 705552
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:

$\sqrt{\Delta}=\sqrt{705552}=\sqrt{16*44097}=\sqrt{16}*\sqrt{44097}=4\sqrt{44097}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-840)-4\sqrt{44097}}{2*4}=\frac{840-4\sqrt{44097}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-840)+4\sqrt{44097}}{2*4}=\frac{840+4\sqrt{44097}}{8}
$