1/4x-11x=-16

Solution for 1/4x-11x=-16 equation:

1/4x-11x=-16

We move all terms to the left:

1/4x-11x-(-16)=0


Domain of the equation: 4x!=0

x!=0/4

x!=0

x∈R


We add all the numbers together, and all the variables

-11x+1/4x+16=0

We multiply all the terms by the denominator


-11x*4x+16*4x+1=0

Wy multiply elements

-44x^2+64x+1=0

a = -44; b = 64; c = +1;
Δ = b2-4ac
Δ = 642-4·(-44)·1
Δ = 4272
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:

$\sqrt{\Delta}=\sqrt{4272}=\sqrt{16*267}=\sqrt{16}*\sqrt{267}=4\sqrt{267}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(64)-4\sqrt{267}}{2*-44}=\frac{-64-4\sqrt{267}}{-88}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(64)+4\sqrt{267}}{2*-44}=\frac{-64+4\sqrt{267}}{-88}
$