4x+(65/2x)=25

Solution for 4x+(65/2x)=25 equation:

4x+(65/2x)=25

We move all terms to the left:

4x+(65/2x)-(25)=0


Domain of the equation: 2x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

4x+(+65/2x)-25=0

We get rid of parentheses

4x+65/2x-25=0

We multiply all the terms by the denominator


4x*2x-25*2x+65=0

Wy multiply elements

8x^2-50x+65=0

a = 8; b = -50; c = +65;
Δ = b2-4ac
Δ = -502-4·8·65
Δ = 420
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:

$\sqrt{\Delta}=\sqrt{420}=\sqrt{4*105}=\sqrt{4}*\sqrt{105}=2\sqrt{105}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-50)-2\sqrt{105}}{2*8}=\frac{50-2\sqrt{105}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-50)+2\sqrt{105}}{2*8}=\frac{50+2\sqrt{105}}{16}
$