7/2x+5-3/10x+10=11/120

Solution for 7/2x+5-3/10x+10=11/120 equation:

7/2x+5-3/10x+10=11/120

We move all terms to the left:

7/2x+5-3/10x+10-(11/120)=0


Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R



Domain of the equation: 10x!=0

x!=0/10

x!=0

x∈R


We add all the numbers together, and all the variables

7/2x-3/10x+5+10-(+11/120)=0

We add all the numbers together, and all the variables

7/2x-3/10x+15-(+11/120)=0

We get rid of parentheses

7/2x-3/10x+15-11/120=0

We calculate fractions


(-220x^2)/2400x^2+8400x/2400x^2+(-720x)/2400x^2+15=0

We multiply all the terms by the denominator


(-220x^2)+8400x+(-720x)+15*2400x^2=0

Wy multiply elements

(-220x^2)+36000x^2+8400x+(-720x)=0

We get rid of parentheses

-220x^2+36000x^2+8400x-720x=0

We add all the numbers together, and all the variables

35780x^2+7680x=0

a = 35780; b = 7680; c = 0;
Δ = b2-4ac
Δ = 76802-4·35780·0
Δ = 58982400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{58982400}=7680$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7680)-7680}{2*35780}=\frac{-15360}{71560}
=-384/1789
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7680)+7680}{2*35780}=\frac{0}{71560}
=0
$