14/2x+125/4x=16

Solution for 14/2x+125/4x=16 equation:

14/2x+125/4x=16

We move all terms to the left:

14/2x+125/4x-(16)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


56x/8x^2+250x/8x^2-16=0

We multiply all the terms by the denominator


56x+250x-16*8x^2=0

We add all the numbers together, and all the variables

306x-16*8x^2=0

Wy multiply elements

-128x^2+306x=0

a = -128; b = 306; c = 0;
Δ = b2-4ac
Δ = 3062-4·(-128)·0
Δ = 93636
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{93636}=306$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(306)-306}{2*-128}=\frac{-612}{-256}
=2+25/64
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(306)+306}{2*-128}=\frac{0}{-256}
=0
$