11a+12a(a+a=184)=2080

Solution for 11a+12a(a+a=184)=2080 equation:

11a+12a(a+a=184)=2080

We move all terms to the left:

11a+12a(a+a-(184))=0

We add all the numbers together, and all the variables

11a+12a(2a-184)=0

We multiply parentheses

24a^2+11a-2208a=0

We add all the numbers together, and all the variables

24a^2-2197a=0

a = 24; b = -2197; c = 0;
Δ = b2-4ac
Δ = -21972-4·24·0
Δ = 4826809
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4826809}=2197$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2197)-2197}{2*24}=\frac{0}{48}
=0
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2197)+2197}{2*24}=\frac{4394}{48}
=91+13/24
$