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

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

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

We move all terms to the left:

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


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 55x!=0

x!=0/55

x!=0

x∈R


We calculate fractions


55x/220x^2+(-4x)/220x^2-9=0

We multiply all the terms by the denominator


55x+(-4x)-9*220x^2=0

Wy multiply elements

-1980x^2+55x+(-4x)=0

We get rid of parentheses

-1980x^2+55x-4x=0

We add all the numbers together, and all the variables

-1980x^2+51x=0

a = -1980; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-1980)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-1980}=\frac{-102}{-3960}
=17/660
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-1980}=\frac{0}{-3960}
=0
$