9/10b-4/5b=6

Solution for 9/10b-4/5b=6 equation:

9/10b-4/5b=6

We move all terms to the left:

9/10b-4/5b-(6)=0


Domain of the equation: 10b!=0

b!=0/10

b!=0

b∈R



Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We calculate fractions


45b/50b^2+(-40b)/50b^2-6=0

We multiply all the terms by the denominator


45b+(-40b)-6*50b^2=0

Wy multiply elements

-300b^2+45b+(-40b)=0

We get rid of parentheses

-300b^2+45b-40b=0

We add all the numbers together, and all the variables

-300b^2+5b=0

a = -300; b = 5; c = 0;
Δ = b2-4ac
Δ = 52-4·(-300)·0
Δ = 25
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{25}=5$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(5)-5}{2*-300}=\frac{-10}{-600}
=1/60
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(5)+5}{2*-300}=\frac{0}{-600}
=0
$