9/4x*2-13/7x+1/16=0

Solution for 9/4x*2-13/7x+1/16=0 equation:

9/4x*2-13/7x+1/16=0


Domain of the equation: 4x*2!=0

x!=0/1

x!=0

x∈R



Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R


We calculate fractions


112x^2/6272x^2+1008x/6272x^2+(-3328x)/6272x^2=0

We multiply all the terms by the denominator


112x^2+1008x+(-3328x)=0

We get rid of parentheses

112x^2+1008x-3328x=0

We add all the numbers together, and all the variables

112x^2-2320x=0

a = 112; b = -2320; c = 0;
Δ = b2-4ac
Δ = -23202-4·112·0
Δ = 5382400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5382400}=2320$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2320)-2320}{2*112}=\frac{0}{224}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2320)+2320}{2*112}=\frac{4640}{224}
=20+5/7
$