2-6/5x+1/10x-4/5=0

Solution for 2-6/5x+1/10x-4/5=0 equation:

2-6/5x+1/10x-4/5=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 calculate fractions


(-60x)/1250x^2+125x/1250x^2+(-40x)/1250x^2+2=0

We multiply all the terms by the denominator


(-60x)+125x+(-40x)+2*1250x^2=0

We add all the numbers together, and all the variables

125x+(-60x)+(-40x)+2*1250x^2=0

Wy multiply elements

2500x^2+125x+(-60x)+(-40x)=0

We get rid of parentheses

2500x^2+125x-60x-40x=0

We add all the numbers together, and all the variables

2500x^2+25x=0

a = 2500; b = 25; c = 0;
Δ = b2-4ac
Δ = 252-4·2500·0
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-25}{2*2500}=\frac{-50}{5000}
=-1/100
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+25}{2*2500}=\frac{0}{5000}
=0
$