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

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

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

We move all terms to the left:

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


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 4x-5)!=0

x∈R


We get rid of parentheses

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

We calculate fractions


8x/12x^2+(-15x)/12x^2+5+16=0

We add all the numbers together, and all the variables

8x/12x^2+(-15x)/12x^2+21=0

We multiply all the terms by the denominator


8x+(-15x)+21*12x^2=0

Wy multiply elements

252x^2+8x+(-15x)=0

We get rid of parentheses

252x^2+8x-15x=0

We add all the numbers together, and all the variables

252x^2-7x=0

a = 252; b = -7; c = 0;
Δ = b2-4ac
Δ = -72-4·252·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-7}{2*252}=\frac{0}{504}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+7}{2*252}=\frac{14}{504}
=1/36
$