2x+3/2x=25

Solution for 2x+3/2x=25 equation:

2x+3/2x=25

We move all terms to the left:

2x+3/2x-(25)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We multiply all the terms by the denominator


2x*2x-25*2x+3=0

Wy multiply elements

4x^2-50x+3=0

a = 4; b = -50; c = +3;
Δ = b2-4ac
Δ = -502-4·4·3
Δ = 2452
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:

$\sqrt{\Delta}=\sqrt{2452}=\sqrt{4*613}=\sqrt{4}*\sqrt{613}=2\sqrt{613}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{613}}{2*4}=\frac{50-2\sqrt{613}}{8}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{613}}{2*4}=\frac{50+2\sqrt{613}}{8}
$