a=5/9a+7

Solution for a=5/9a+7 equation:

a=5/9a+7

We move all terms to the left:

a-(5/9a+7)=0


Domain of the equation: 9a+7)!=0

a∈R


We get rid of parentheses

a-5/9a-7=0

We multiply all the terms by the denominator


a*9a-7*9a-5=0

Wy multiply elements

9a^2-63a-5=0

a = 9; b = -63; c = -5;
Δ = b2-4ac
Δ = -632-4·9·(-5)
Δ = 4149
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:

$\sqrt{\Delta}=\sqrt{4149}=\sqrt{9*461}=\sqrt{9}*\sqrt{461}=3\sqrt{461}$
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-63)-3\sqrt{461}}{2*9}=\frac{63-3\sqrt{461}}{18}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-63)+3\sqrt{461}}{2*9}=\frac{63+3\sqrt{461}}{18}
$