245-9/8b=5b

Solution for 245-9/8b=5b equation:

245-9/8b=5b

We move all terms to the left:

245-9/8b-(5b)=0


Domain of the equation: 8b!=0

b!=0/8

b!=0

b∈R


We add all the numbers together, and all the variables

-5b-9/8b+245=0

We multiply all the terms by the denominator


-5b*8b+245*8b-9=0

Wy multiply elements

-40b^2+1960b-9=0

a = -40; b = 1960; c = -9;
Δ = b2-4ac
Δ = 19602-4·(-40)·(-9)
Δ = 3840160
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:

$\sqrt{\Delta}=\sqrt{3840160}=\sqrt{16*240010}=\sqrt{16}*\sqrt{240010}=4\sqrt{240010}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1960)-4\sqrt{240010}}{2*-40}=\frac{-1960-4\sqrt{240010}}{-80}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1960)+4\sqrt{240010}}{2*-40}=\frac{-1960+4\sqrt{240010}}{-80}
$