(7/5x+5)-(3/10x+10)=11/120

Solution for (7/5x+5)-(3/10x+10)=11/120 equation:

(7/5x+5)-(3/10x+10)=11/120

We move all terms to the left:

(7/5x+5)-(3/10x+10)-(11/120)=0


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

x∈R



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

x∈R


We add all the numbers together, and all the variables

(7/5x+5)-(3/10x+10)-(+11/120)=0

We get rid of parentheses

7/5x-3/10x+5-10-11/120=0

We calculate fractions


(-550x^2)/6000x^2+8400x/6000x^2+(-1800x)/6000x^2+5-10=0

We add all the numbers together, and all the variables

(-550x^2)/6000x^2+8400x/6000x^2+(-1800x)/6000x^2-5=0

We multiply all the terms by the denominator


(-550x^2)+8400x+(-1800x)-5*6000x^2=0

Wy multiply elements

(-550x^2)-30000x^2+8400x+(-1800x)=0

We get rid of parentheses

-550x^2-30000x^2+8400x-1800x=0

We add all the numbers together, and all the variables

-30550x^2+6600x=0

a = -30550; b = 6600; c = 0;
Δ = b2-4ac
Δ = 66002-4·(-30550)·0
Δ = 43560000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{43560000}=6600$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(6600)-6600}{2*-30550}=\frac{-13200}{-61100}
=132/611
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(6600)+6600}{2*-30550}=\frac{0}{-61100}
=0
$