1/4x+1/16x=10

Solution for 1/4x+1/16x=10 equation:

1/4x+1/16x=10

We move all terms to the left:

1/4x+1/16x-(10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R



Domain of the equation: 16x!=0

x!=0/16

x!=0

x∈R


We calculate fractions


16x/64x^2+4x/64x^2-10=0

We multiply all the terms by the denominator


16x+4x-10*64x^2=0

We add all the numbers together, and all the variables

20x-10*64x^2=0

Wy multiply elements

-640x^2+20x=0

a = -640; b = 20; c = 0;
Δ = b2-4ac
Δ = 202-4·(-640)·0
Δ = 400
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{400}=20$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-20}{2*-640}=\frac{-40}{-1280}
=1/32
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+20}{2*-640}=\frac{0}{-1280}
=0
$