2/3*X+16=3/4*x

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

2/3X+16=3/4X

We move all terms to the left:

2/3X+16-(3/4X)=0


Domain of the equation: 3X!=0

X!=0/3

X!=0

X∈R



Domain of the equation: 4X)!=0

X!=0/1

X!=0

X∈R


We add all the numbers together, and all the variables

2/3X-(+3/4X)+16=0

We get rid of parentheses

2/3X-3/4X+16=0

We calculate fractions


8X/12X^2+(-9X)/12X^2+16=0

We multiply all the terms by the denominator


8X+(-9X)+16*12X^2=0

Wy multiply elements

192X^2+8X+(-9X)=0

We get rid of parentheses

192X^2+8X-9X=0

We add all the numbers together, and all the variables

192X^2-1X=0

a = 192; b = -1; c = 0;
Δ = b2-4ac
Δ = -12-4·192·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-1}{2*192}=\frac{0}{384}
=0
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+1}{2*192}=\frac{2}{384}
=1/192
$