3/11a-a=4

Solution for 3/11a-a=4 equation:

3/11a-a=4

We move all terms to the left:

3/11a-a-(4)=0


Domain of the equation: 11a!=0

a!=0/11

a!=0

a∈R


We add all the numbers together, and all the variables

-1a+3/11a-4=0

We multiply all the terms by the denominator


-1a*11a-4*11a+3=0

Wy multiply elements

-11a^2-44a+3=0

a = -11; b = -44; c = +3;
Δ = b2-4ac
Δ = -442-4·(-11)·3
Δ = 2068
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{2068}=\sqrt{4*517}=\sqrt{4}*\sqrt{517}=2\sqrt{517}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-44)-2\sqrt{517}}{2*-11}=\frac{44-2\sqrt{517}}{-22}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-44)+2\sqrt{517}}{2*-11}=\frac{44+2\sqrt{517}}{-22}
$