-6/7x-5/21x+1/3=-80

Solution for -6/7x-5/21x+1/3=-80 equation:

-6/7x-5/21x+1/3=-80

We move all terms to the left:

-6/7x-5/21x+1/3-(-80)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 21x!=0

x!=0/21

x!=0

x∈R


We add all the numbers together, and all the variables

-6/7x-5/21x+80+1/3=0

We calculate fractions


294x^2/1323x^2+(-1134x)/1323x^2+(-315x)/1323x^2+80=0

We multiply all the terms by the denominator


294x^2+(-1134x)+(-315x)+80*1323x^2=0

Wy multiply elements

294x^2+105840x^2+(-1134x)+(-315x)=0

We get rid of parentheses

294x^2+105840x^2-1134x-315x=0

We add all the numbers together, and all the variables

106134x^2-1449x=0

a = 106134; b = -1449; c = 0;
Δ = b2-4ac
Δ = -14492-4·106134·0
Δ = 2099601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2099601}=1449$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1449)-1449}{2*106134}=\frac{0}{212268}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1449)+1449}{2*106134}=\frac{2898}{212268}
=69/5054
$