a=3/7a+5

Solution for a=3/7a+5 equation:

a=3/7a+5

We move all terms to the left:

a-(3/7a+5)=0


Domain of the equation: 7a+5)!=0

a∈R


We get rid of parentheses

a-3/7a-5=0

We multiply all the terms by the denominator


a*7a-5*7a-3=0

Wy multiply elements

7a^2-35a-3=0

a = 7; b = -35; c = -3;
Δ = b2-4ac
Δ = -352-4·7·(-3)
Δ = 1309
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$a_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-\sqrt{1309}}{2*7}=\frac{35-\sqrt{1309}}{14}
$
$a_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+\sqrt{1309}}{2*7}=\frac{35+\sqrt{1309}}{14}
$