2/5x-10=8/11x+8

Solution for 2/5x-10=8/11x+8 equation:

2/5x-10=8/11x+8

We move all terms to the left:

2/5x-10-(8/11x+8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 11x+8)!=0

x∈R


We get rid of parentheses

2/5x-8/11x-8-10=0

We calculate fractions


22x/55x^2+(-40x)/55x^2-8-10=0

We add all the numbers together, and all the variables

22x/55x^2+(-40x)/55x^2-18=0

We multiply all the terms by the denominator


22x+(-40x)-18*55x^2=0

Wy multiply elements

-990x^2+22x+(-40x)=0

We get rid of parentheses

-990x^2+22x-40x=0

We add all the numbers together, and all the variables

-990x^2-18x=0

a = -990; b = -18; c = 0;
Δ = b2-4ac
Δ = -182-4·(-990)·0
Δ = 324
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{324}=18$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-18)-18}{2*-990}=\frac{0}{-1980}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-18)+18}{2*-990}=\frac{36}{-1980}
=-1/55
$