1/5x+1/4x=10

Solution for 1/5x+1/4x=10 equation:

1/5x+1/4x=10

We move all terms to the left:

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


Domain of the equation: 5x!=0

x!=0/5

x!=0

x∈R



Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We calculate fractions


4x/20x^2+5x/20x^2-10=0

We multiply all the terms by the denominator


4x+5x-10*20x^2=0

We add all the numbers together, and all the variables

9x-10*20x^2=0

Wy multiply elements

-200x^2+9x=0

a = -200; b = 9; c = 0;
Δ = b2-4ac
Δ = 92-4·(-200)·0
Δ = 81
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{81}=9$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(9)-9}{2*-200}=\frac{-18}{-400}
=9/200
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+9}{2*-200}=\frac{0}{-400}
=0
$