-b+8/5b=9

Solution for -b+8/5b=9 equation:

-b+8/5b=9

We move all terms to the left:

-b+8/5b-(9)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We add all the numbers together, and all the variables

-1b+8/5b-9=0

We multiply all the terms by the denominator


-1b*5b-9*5b+8=0

Wy multiply elements

-5b^2-45b+8=0

a = -5; b = -45; c = +8;
Δ = b2-4ac
Δ = -452-4·(-5)·8
Δ = 2185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-\sqrt{2185}}{2*-5}=\frac{45-\sqrt{2185}}{-10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+\sqrt{2185}}{2*-5}=\frac{45+\sqrt{2185}}{-10}
$