49-2/3x=32-1/16x

Solution for 49-2/3x=32-1/16x equation:

49-2/3x=32-1/16x

We move all terms to the left:

49-2/3x-(32-1/16x)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 16x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-2/3x-(-1/16x+32)+49=0

We get rid of parentheses

-2/3x+1/16x-32+49=0

We calculate fractions


(-32x)/48x^2+3x/48x^2-32+49=0

We add all the numbers together, and all the variables

(-32x)/48x^2+3x/48x^2+17=0

We multiply all the terms by the denominator


(-32x)+3x+17*48x^2=0

We add all the numbers together, and all the variables

3x+(-32x)+17*48x^2=0

Wy multiply elements

816x^2+3x+(-32x)=0

We get rid of parentheses

816x^2+3x-32x=0

We add all the numbers together, and all the variables

816x^2-29x=0

a = 816; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·816·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*816}=\frac{0}{1632}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*816}=\frac{58}{1632}
=29/816
$