2/3x+1=7/16x+3

Solution for 2/3x+1=7/16x+3 equation:

2/3x+1=7/16x+3

We move all terms to the left:

2/3x+1-(7/16x+3)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R



Domain of the equation: 16x+3)!=0

x∈R


We get rid of parentheses

2/3x-7/16x-3+1=0

We calculate fractions


32x/48x^2+(-21x)/48x^2-3+1=0

We add all the numbers together, and all the variables

32x/48x^2+(-21x)/48x^2-2=0

We multiply all the terms by the denominator


32x+(-21x)-2*48x^2=0

Wy multiply elements

-96x^2+32x+(-21x)=0

We get rid of parentheses

-96x^2+32x-21x=0

We add all the numbers together, and all the variables

-96x^2+11x=0

a = -96; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-96)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-96}=\frac{-22}{-192}
=11/96
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-96}=\frac{0}{-192}
=0
$