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

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

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

We move all terms to the left:

-1/5x-5/4-9/10x-(1/4)=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 add all the numbers together, and all the variables

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

We get rid of parentheses

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

We calculate fractions


(-50x^2-5)/800x^2+(-160x)/800x^2+(-720x)/800x^2=0

We multiply all the terms by the denominator


(-50x^2-5)+(-160x)+(-720x)=0

We get rid of parentheses

-50x^2-160x-720x-5=0

We add all the numbers together, and all the variables

-50x^2-880x-5=0

a = -50; b = -880; c = -5;
Δ = b2-4ac
Δ = -8802-4·(-50)·(-5)
Δ = 773400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{773400}=\sqrt{100*7734}=\sqrt{100}*\sqrt{7734}=10\sqrt{7734}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-880)-10\sqrt{7734}}{2*-50}=\frac{880-10\sqrt{7734}}{-100}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-880)+10\sqrt{7734}}{2*-50}=\frac{880+10\sqrt{7734}}{-100}
$