1/4x-8x=-10

Solution for 1/4x-8x=-10 equation:

1/4x-8x=-10

We move all terms to the left:

1/4x-8x-(-10)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-8x+1/4x+10=0

We multiply all the terms by the denominator


-8x*4x+10*4x+1=0

Wy multiply elements

-32x^2+40x+1=0

a = -32; b = 40; c = +1;
Δ = b2-4ac
Δ = 402-4·(-32)·1
Δ = 1728
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:

$\sqrt{\Delta}=\sqrt{1728}=\sqrt{576*3}=\sqrt{576}*\sqrt{3}=24\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(40)-24\sqrt{3}}{2*-32}=\frac{-40-24\sqrt{3}}{-64}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(40)+24\sqrt{3}}{2*-32}=\frac{-40+24\sqrt{3}}{-64}
$