9/11a=-5a+21

Solution for 9/11a=-5a+21 equation:

9/11a=-5a+21

We move all terms to the left:

9/11a-(-5a+21)=0


Domain of the equation: 11a!=0

a!=0/11

a!=0

a∈R


We get rid of parentheses

9/11a+5a-21=0

We multiply all the terms by the denominator


5a*11a-21*11a+9=0

Wy multiply elements

55a^2-231a+9=0

a = 55; b = -231; c = +9;
Δ = b2-4ac
Δ = -2312-4·55·9
Δ = 51381
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:

$\sqrt{\Delta}=\sqrt{51381}=\sqrt{9*5709}=\sqrt{9}*\sqrt{5709}=3\sqrt{5709}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-231)-3\sqrt{5709}}{2*55}=\frac{231-3\sqrt{5709}}{110}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-231)+3\sqrt{5709}}{2*55}=\frac{231+3\sqrt{5709}}{110}
$