3/5+4/5x+7/10x+11/2=53/5

Solution for 3/5+4/5x+7/10x+11/2=53/5 equation:

3/5+4/5x+7/10x+11/2=53/5

We move all terms to the left:

3/5+4/5x+7/10x+11/2-(53/5)=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 add all the numbers together, and all the variables

4/5x+7/10x+3/5+11/2-(+53/5)=0

We get rid of parentheses

4/5x+7/10x+3/5+11/2-53/5=0

We calculate fractions


2750x^2/2500x^2+160x/2500x^2+1750x/2500x^2+(-2120x+3)/2500x^2=0

We multiply all the terms by the denominator


2750x^2+160x+1750x+(-2120x+3)=0

We add all the numbers together, and all the variables

2750x^2+1910x+(-2120x+3)=0

We get rid of parentheses

2750x^2+1910x-2120x+3=0

We add all the numbers together, and all the variables

2750x^2-210x+3=0

a = 2750; b = -210; c = +3;
Δ = b2-4ac
Δ = -2102-4·2750·3
Δ = 11100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{11100}=\sqrt{100*111}=\sqrt{100}*\sqrt{111}=10\sqrt{111}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-210)-10\sqrt{111}}{2*2750}=\frac{210-10\sqrt{111}}{5500}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-210)+10\sqrt{111}}{2*2750}=\frac{210+10\sqrt{111}}{5500}
$