6/7x+4=2/11x+16

Solution for 6/7x+4=2/11x+16 equation:

6/7x+4=2/11x+16

We move all terms to the left:

6/7x+4-(2/11x+16)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 11x+16)!=0

x∈R


We get rid of parentheses

6/7x-2/11x-16+4=0

We calculate fractions


66x/77x^2+(-14x)/77x^2-16+4=0

We add all the numbers together, and all the variables

66x/77x^2+(-14x)/77x^2-12=0

We multiply all the terms by the denominator


66x+(-14x)-12*77x^2=0

Wy multiply elements

-924x^2+66x+(-14x)=0

We get rid of parentheses

-924x^2+66x-14x=0

We add all the numbers together, and all the variables

-924x^2+52x=0

a = -924; b = 52; c = 0;
Δ = b2-4ac
Δ = 522-4·(-924)·0
Δ = 2704
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2704}=52$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(52)-52}{2*-924}=\frac{-104}{-1848}
=13/231
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(52)+52}{2*-924}=\frac{0}{-1848}
=0
$