9+2/5b=7/6b

Solution for 9+2/5b=7/6b equation:

9+2/5b=7/6b

We move all terms to the left:

9+2/5b-(7/6b)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 6b)!=0

b!=0/1

b!=0

b∈R


We add all the numbers together, and all the variables

2/5b-(+7/6b)+9=0

We get rid of parentheses

2/5b-7/6b+9=0

We calculate fractions


12b/30b^2+(-35b)/30b^2+9=0

We multiply all the terms by the denominator


12b+(-35b)+9*30b^2=0

Wy multiply elements

270b^2+12b+(-35b)=0

We get rid of parentheses

270b^2+12b-35b=0

We add all the numbers together, and all the variables

270b^2-23b=0

a = 270; b = -23; c = 0;
Δ = b2-4ac
Δ = -232-4·270·0
Δ = 529
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{529}=23$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-23)-23}{2*270}=\frac{0}{540}
=0
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-23)+23}{2*270}=\frac{46}{540}
=23/270
$