3/7x+1/3x=32
We move all terms to the left:
3/7x+1/3x-(32)=0
Domain of the equation: 7x!=0
x!=0/7
x!=0
x∈R
Domain of the equation: 3x!=0
x!=0/3
x!=0
x∈R
We calculate fractions
9x/21x^2+7x/21x^2-32=0
We multiply all the terms by the denominator
9x+7x-32*21x^2=0
We add all the numbers together, and all the variables
16x-32*21x^2=0
Wy multiply elements
-672x^2+16x=0
a = -672; b = 16; c = 0;
Δ = b2-4ac
Δ = 162-4·(-672)·0
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
x1=−b−Δ√2ax2=−b+Δ√2a
Δ−−√=256−−−√=16
x1=−b−Δ√2a=−(16)−162∗−672=−32−1344=1/42
x2=−b+Δ√2a=−(16)+162∗−672=0−1344=0
