4/7x-3/11x=11

Solution for 4/7x-3/11x=11 equation:

4/7x-3/11x=11

We move all terms to the left:

4/7x-3/11x-(11)=0


Domain of the equation: 7x!=0

x!=0/7

x!=0

x∈R



Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R


We calculate fractions


44x/77x^2+(-21x)/77x^2-11=0

We multiply all the terms by the denominator


44x+(-21x)-11*77x^2=0

Wy multiply elements

-847x^2+44x+(-21x)=0

We get rid of parentheses

-847x^2+44x-21x=0

We add all the numbers together, and all the variables

-847x^2+23x=0

a = -847; b = 23; c = 0;
Δ = b2-4ac
Δ = 232-4·(-847)·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(23)-23}{2*-847}=\frac{-46}{-1694}
=23/847
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(23)+23}{2*-847}=\frac{0}{-1694}
=0
$