8/3b+5/6b=5

Solution for 8/3b+5/6b=5 equation:

8/3b+5/6b=5

We move all terms to the left:

8/3b+5/6b-(5)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R



Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R


We calculate fractions


48b/18b^2+15b/18b^2-5=0

We multiply all the terms by the denominator


48b+15b-5*18b^2=0

We add all the numbers together, and all the variables

63b-5*18b^2=0

Wy multiply elements

-90b^2+63b=0

a = -90; b = 63; c = 0;
Δ = b2-4ac
Δ = 632-4·(-90)·0
Δ = 3969
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3969}=63$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(63)-63}{2*-90}=\frac{-126}{-180}
=7/10
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(63)+63}{2*-90}=\frac{0}{-180}
=0
$