2/5+3/4x+5/2x=16

Solution for 2/5+3/4x+5/2x=16 equation:

2/5+3/4x+5/2x=16

We move all terms to the left:

2/5+3/4x+5/2x-(16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


determiningTheFunctionDomain
3/4x+5/2x-16+2/5=0

We calculate fractions


32x^2/200x^2+150x/200x^2+500x/200x^2-16=0

We multiply all the terms by the denominator


32x^2+150x+500x-16*200x^2=0

We add all the numbers together, and all the variables

32x^2+650x-16*200x^2=0

Wy multiply elements

32x^2-3200x^2+650x=0

We add all the numbers together, and all the variables

-3168x^2+650x=0

a = -3168; b = 650; c = 0;
Δ = b2-4ac
Δ = 6502-4·(-3168)·0
Δ = 422500
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{422500}=650$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(650)-650}{2*-3168}=\frac{-1300}{-6336}
=325/1584
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(650)+650}{2*-3168}=\frac{0}{-6336}
=0
$