50-l=1/2l-4

Solution for 50-l=1/2l-4 equation:

50-l=1/2l-4

We move all terms to the left:

50-l-(1/2l-4)=0


Domain of the equation: 2l-4)!=0

l∈R


We add all the numbers together, and all the variables

-1l-(1/2l-4)+50=0

We get rid of parentheses

-1l-1/2l+4+50=0

We multiply all the terms by the denominator


-1l*2l+4*2l+50*2l-1=0

Wy multiply elements

-2l^2+8l+100l-1=0

We add all the numbers together, and all the variables

-2l^2+108l-1=0

a = -2; b = 108; c = -1;
Δ = b2-4ac
Δ = 1082-4·(-2)·(-1)
Δ = 11656
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:

$\sqrt{\Delta}=\sqrt{11656}=\sqrt{4*2914}=\sqrt{4}*\sqrt{2914}=2\sqrt{2914}$
$l_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(108)-2\sqrt{2914}}{2*-2}=\frac{-108-2\sqrt{2914}}{-4}
$
$l_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(108)+2\sqrt{2914}}{2*-2}=\frac{-108+2\sqrt{2914}}{-4}
$