11-9/10x=7-1/5x

Solution for 11-9/10x=7-1/5x equation:

11-9/10x=7-1/5x

We move all terms to the left:

11-9/10x-(7-1/5x)=0


Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R



Domain of the equation: 5x)!=0

x!=0/1

x!=0

x∈R


We add all the numbers together, and all the variables

-9/10x-(-1/5x+7)+11=0

We get rid of parentheses

-9/10x+1/5x-7+11=0

We calculate fractions


(-45x)/50x^2+10x/50x^2-7+11=0

We add all the numbers together, and all the variables

(-45x)/50x^2+10x/50x^2+4=0

We multiply all the terms by the denominator


(-45x)+10x+4*50x^2=0

We add all the numbers together, and all the variables

10x+(-45x)+4*50x^2=0

Wy multiply elements

200x^2+10x+(-45x)=0

We get rid of parentheses

200x^2+10x-45x=0

We add all the numbers together, and all the variables

200x^2-35x=0

a = 200; b = -35; c = 0;
Δ = b2-4ac
Δ = -352-4·200·0
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-35}{2*200}=\frac{0}{400}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+35}{2*200}=\frac{70}{400}
=7/40
$