4/5x-4=9/10x-1

Solution for 4/5x-4=9/10x-1 equation:

4/5x-4=9/10x-1

We move all terms to the left:

4/5x-4-(9/10x-1)=0


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 10x-1)!=0

x∈R


We get rid of parentheses

4/5x-9/10x+1-4=0

We calculate fractions


40x/50x^2+(-45x)/50x^2+1-4=0

We add all the numbers together, and all the variables

40x/50x^2+(-45x)/50x^2-3=0

We multiply all the terms by the denominator


40x+(-45x)-3*50x^2=0

Wy multiply elements

-150x^2+40x+(-45x)=0

We get rid of parentheses

-150x^2+40x-45x=0

We add all the numbers together, and all the variables

-150x^2-5x=0

a = -150; b = -5; c = 0;
Δ = b2-4ac
Δ = -52-4·(-150)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-5)-5}{2*-150}=\frac{0}{-300}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+5}{2*-150}=\frac{10}{-300}
=-1/30
$