6/5b+3/6b=90

Solution for 6/5b+3/6b=90 equation:

6/5b+3/6b=90

We move all terms to the left:

6/5b+3/6b-(90)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 6b!=0

b!=0/6

b!=0

b∈R


We calculate fractions


36b/30b^2+15b/30b^2-90=0

We multiply all the terms by the denominator


36b+15b-90*30b^2=0

We add all the numbers together, and all the variables

51b-90*30b^2=0

Wy multiply elements

-2700b^2+51b=0

a = -2700; b = 51; c = 0;
Δ = b2-4ac
Δ = 512-4·(-2700)·0
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(51)-51}{2*-2700}=\frac{-102}{-5400}
=17/900
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(51)+51}{2*-2700}=\frac{0}{-5400}
=0
$