7/5x+9/10+1/10x=5/8

Solution for 7/5x+9/10+1/10x=5/8 equation:

7/5x+9/10+1/10x=5/8

We move all terms to the left:

7/5x+9/10+1/10x-(5/8)=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

7/5x+1/10x+9/10-(+5/8)=0

We get rid of parentheses

7/5x+1/10x+9/10-5/8=0

We calculate fractions


(-2500x^2)/4000x^2+5600x/4000x^2+320x/4000x^2+2880x/4000x^2=0

We multiply all the terms by the denominator


(-2500x^2)+5600x+320x+2880x=0

We add all the numbers together, and all the variables

(-2500x^2)+8800x=0

We get rid of parentheses

-2500x^2+8800x=0

a = -2500; b = 8800; c = 0;
Δ = b2-4ac
Δ = 88002-4·(-2500)·0
Δ = 77440000
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{77440000}=8800$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(8800)-8800}{2*-2500}=\frac{-17600}{-5000}
=3+13/25
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(8800)+8800}{2*-2500}=\frac{0}{-5000}
=0
$