10/5x+8/5x-3/2x=1

Solution for 10/5x+8/5x-3/2x=1 equation:

10/5x+8/5x-3/2x=1

We move all terms to the left:

10/5x+8/5x-3/2x-(1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 2x!=0

x!=0/2

x!=0

x∈R


We calculate fractions


(16x+10)/10x^2+(-15x)/10x^2-1=0

We multiply all the terms by the denominator


(16x+10)+(-15x)-1*10x^2=0

Wy multiply elements

-10x^2+(16x+10)+(-15x)=0

We get rid of parentheses

-10x^2+16x-15x+10=0

We add all the numbers together, and all the variables

-10x^2+x+10=0

a = -10; b = 1; c = +10;
Δ = b2-4ac
Δ = 12-4·(-10)·10
Δ = 401
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{401}}{2*-10}=\frac{-1-\sqrt{401}}{-20}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{401}}{2*-10}=\frac{-1+\sqrt{401}}{-20}
$