1/4l-7l=16

Solution for 1/4l-7l=16 equation:

1/4l-7l=16

We move all terms to the left:

1/4l-7l-(16)=0


Domain of the equation: 4l!=0

l!=0/4

l!=0

l∈R


We add all the numbers together, and all the variables

-7l+1/4l-16=0

We multiply all the terms by the denominator


-7l*4l-16*4l+1=0

Wy multiply elements

-28l^2-64l+1=0

a = -28; b = -64; c = +1;
Δ = b2-4ac
Δ = -642-4·(-28)·1
Δ = 4208
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{4208}=\sqrt{16*263}=\sqrt{16}*\sqrt{263}=4\sqrt{263}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-4\sqrt{263}}{2*-28}=\frac{64-4\sqrt{263}}{-56}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+4\sqrt{263}}{2*-28}=\frac{64+4\sqrt{263}}{-56}
$