4-1/5x=1/10x-8

Solution for 4-1/5x=1/10x-8 equation:

4-1/5x=1/10x-8

We move all terms to the left:

4-1/5x-(1/10x-8)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-8)!=0

x∈R


We get rid of parentheses

-1/5x-1/10x+8+4=0

We calculate fractions


(-10x)/50x^2+(-5x)/50x^2+8+4=0

We add all the numbers together, and all the variables

(-10x)/50x^2+(-5x)/50x^2+12=0

We multiply all the terms by the denominator


(-10x)+(-5x)+12*50x^2=0

Wy multiply elements

600x^2+(-10x)+(-5x)=0

We get rid of parentheses

600x^2-10x-5x=0

We add all the numbers together, and all the variables

600x^2-15x=0

a = 600; b = -15; c = 0;
Δ = b2-4ac
Δ = -152-4·600·0
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-15)-15}{2*600}=\frac{0}{1200}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-15)+15}{2*600}=\frac{30}{1200}
=1/40
$