1/7x+1/8x+1/7=83/56

Solution for 1/7x+1/8x+1/7=83/56 equation:

1/7x+1/8x+1/7=83/56

We move all terms to the left:

1/7x+1/8x+1/7-(83/56)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 8x!=0

x!=0/8

x!=0

x∈R


We add all the numbers together, and all the variables

1/7x+1/8x+1/7-(+83/56)=0

We get rid of parentheses

1/7x+1/8x+1/7-83/56=0

We calculate fractions


(-260288x^2)/153664x^2+2240x/153664x^2+19208x/153664x^2+2240x/153664x^2=0

We multiply all the terms by the denominator


(-260288x^2)+2240x+19208x+2240x=0

We add all the numbers together, and all the variables

(-260288x^2)+23688x=0

We get rid of parentheses

-260288x^2+23688x=0

a = -260288; b = 23688; c = 0;
Δ = b2-4ac
Δ = 236882-4·(-260288)·0
Δ = 561121344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{561121344}=23688$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23688)-23688}{2*-260288}=\frac{-47376}{-520576}
=423/4648
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23688)+23688}{2*-260288}=\frac{0}{-520576}
=0
$