6/11x=10-4/5x.x=0

Solution for 6/11x=10-4/5x.x=0 equation:

6/11x=10-4/5x.x=0

We move all terms to the left:

6/11x-(10-4/5x.x)=0


Domain of the equation: 11x!=0

x!=0/11

x!=0

x∈R



Domain of the equation: 5x.x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

6/11x-(-4/5x.x+10)=0

We get rid of parentheses

6/11x+4/5x.x-10=0

We calculate fractions


30x/55x^2+44x/55x^2-10=0

We multiply all the terms by the denominator


30x+44x-10*55x^2=0

We add all the numbers together, and all the variables

74x-10*55x^2=0

Wy multiply elements

-550x^2+74x=0

a = -550; b = 74; c = 0;
Δ = b2-4ac
Δ = 742-4·(-550)·0
Δ = 5476
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{5476}=74$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(74)-74}{2*-550}=\frac{-148}{-1100}
=37/275
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(74)+74}{2*-550}=\frac{0}{-1100}
=0
$