1/16x+3/4x=17/2

Solution for 1/16x+3/4x=17/2 equation:

1/16x+3/4x=17/2

We move all terms to the left:

1/16x+3/4x-(17/2)=0


Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

1/16x+3/4x-(+17/2)=0

We get rid of parentheses

1/16x+3/4x-17/2=0

We calculate fractions


(-4352x^2)/256x^2+16x/256x^2+192x/256x^2=0

We multiply all the terms by the denominator


(-4352x^2)+16x+192x=0

We add all the numbers together, and all the variables

(-4352x^2)+208x=0

We get rid of parentheses

-4352x^2+208x=0

a = -4352; b = 208; c = 0;
Δ = b2-4ac
Δ = 2082-4·(-4352)·0
Δ = 43264
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43264}=208$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(208)-208}{2*-4352}=\frac{-416}{-8704}
=13/272
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(208)+208}{2*-4352}=\frac{0}{-8704}
=0
$