b+7/9b=32

Solution for b+7/9b=32 equation:

b+7/9b=32

We move all terms to the left:

b+7/9b-(32)=0


Domain of the equation: 9b!=0

b!=0/9

b!=0

b∈R


We multiply all the terms by the denominator


b*9b-32*9b+7=0

Wy multiply elements

9b^2-288b+7=0

a = 9; b = -288; c = +7;
Δ = b2-4ac
Δ = -2882-4·9·7
Δ = 82692
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{82692}=\sqrt{36*2297}=\sqrt{36}*\sqrt{2297}=6\sqrt{2297}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-288)-6\sqrt{2297}}{2*9}=\frac{288-6\sqrt{2297}}{18}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-288)+6\sqrt{2297}}{2*9}=\frac{288+6\sqrt{2297}}{18}
$