3/11a-11=7a+99

Solution for 3/11a-11=7a+99 equation:

3/11a-11=7a+99

We move all terms to the left:

3/11a-11-(7a+99)=0


Domain of the equation: 11a!=0

a!=0/11

a!=0

a∈R


We get rid of parentheses

3/11a-7a-99-11=0

We multiply all the terms by the denominator


-7a*11a-99*11a-11*11a+3=0

Wy multiply elements

-77a^2-1089a-121a+3=0

We add all the numbers together, and all the variables

-77a^2-1210a+3=0

a = -77; b = -1210; c = +3;
Δ = b2-4ac
Δ = -12102-4·(-77)·3
Δ = 1465024
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:

$\sqrt{\Delta}=\sqrt{1465024}=\sqrt{64*22891}=\sqrt{64}*\sqrt{22891}=8\sqrt{22891}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1210)-8\sqrt{22891}}{2*-77}=\frac{1210-8\sqrt{22891}}{-154}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1210)+8\sqrt{22891}}{2*-77}=\frac{1210+8\sqrt{22891}}{-154}
$