21/5x+11/10x=11

Solution for 21/5x+11/10x=11 equation:

21/5x+11/10x=11

We move all terms to the left:

21/5x+11/10x-(11)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We calculate fractions


210x/50x^2+55x/50x^2-11=0

We multiply all the terms by the denominator


210x+55x-11*50x^2=0

We add all the numbers together, and all the variables

265x-11*50x^2=0

Wy multiply elements

-550x^2+265x=0

a = -550; b = 265; c = 0;
Δ = b2-4ac
Δ = 2652-4·(-550)·0
Δ = 70225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{70225}=265$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(265)-265}{2*-550}=\frac{-530}{-1100}
=53/110
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(265)+265}{2*-550}=\frac{0}{-1100}
=0
$