1/5x-9=8/11x+7

Solution for 1/5x-9=8/11x+7 equation:

1/5x-9=8/11x+7

We move all terms to the left:

1/5x-9-(8/11x+7)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 11x+7)!=0

x∈R


We get rid of parentheses

1/5x-8/11x-7-9=0

We calculate fractions


11x/55x^2+(-40x)/55x^2-7-9=0

We add all the numbers together, and all the variables

11x/55x^2+(-40x)/55x^2-16=0

We multiply all the terms by the denominator


11x+(-40x)-16*55x^2=0

Wy multiply elements

-880x^2+11x+(-40x)=0

We get rid of parentheses

-880x^2+11x-40x=0

We add all the numbers together, and all the variables

-880x^2-29x=0

a = -880; b = -29; c = 0;
Δ = b2-4ac
Δ = -292-4·(-880)·0
Δ = 841
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{841}=29$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-29)-29}{2*-880}=\frac{0}{-1760}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-29)+29}{2*-880}=\frac{58}{-1760}
=-29/880
$