22/10x+2=3/5x+10

Solution for 22/10x+2=3/5x+10 equation:

22/10x+2=3/5x+10

We move all terms to the left:

22/10x+2-(3/5x+10)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x+10)!=0

x∈R


We get rid of parentheses

22/10x-3/5x-10+2=0

We calculate fractions


110x/50x^2+(-30x)/50x^2-10+2=0

We add all the numbers together, and all the variables

110x/50x^2+(-30x)/50x^2-8=0

We multiply all the terms by the denominator


110x+(-30x)-8*50x^2=0

Wy multiply elements

-400x^2+110x+(-30x)=0

We get rid of parentheses

-400x^2+110x-30x=0

We add all the numbers together, and all the variables

-400x^2+80x=0

a = -400; b = 80; c = 0;
Δ = b2-4ac
Δ = 802-4·(-400)·0
Δ = 6400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{6400}=80$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(80)-80}{2*-400}=\frac{-160}{-800}
=1/5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(80)+80}{2*-400}=\frac{0}{-800}
=0
$