b=45/8b-34

Solution for b=45/8b-34 equation:

b=45/8b-34

We move all terms to the left:

b-(45/8b-34)=0


Domain of the equation: 8b-34)!=0

b∈R


We get rid of parentheses

b-45/8b+34=0

We multiply all the terms by the denominator


b*8b+34*8b-45=0

Wy multiply elements

8b^2+272b-45=0

a = 8; b = 272; c = -45;
Δ = b2-4ac
Δ = 2722-4·8·(-45)
Δ = 75424
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:

$\sqrt{\Delta}=\sqrt{75424}=\sqrt{16*4714}=\sqrt{16}*\sqrt{4714}=4\sqrt{4714}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(272)-4\sqrt{4714}}{2*8}=\frac{-272-4\sqrt{4714}}{16}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(272)+4\sqrt{4714}}{2*8}=\frac{-272+4\sqrt{4714}}{16}
$