(3)/(4)b-(1)/(5)b=11

Solution for (3)/(4)b-(1)/(5)b=11 equation:

(3)/(4)b-(1)/(5)b=11

We move all terms to the left:

(3)/(4)b-(1)/(5)b-(11)=0


Domain of the equation: 4b!=0

b!=0/4

b!=0

b∈R



Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R


We calculate fractions


15b/20b^2+(-4b)/20b^2-11=0

We multiply all the terms by the denominator


15b+(-4b)-11*20b^2=0

Wy multiply elements

-220b^2+15b+(-4b)=0

We get rid of parentheses

-220b^2+15b-4b=0

We add all the numbers together, and all the variables

-220b^2+11b=0

a = -220; b = 11; c = 0;
Δ = b2-4ac
Δ = 112-4·(-220)·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(11)-11}{2*-220}=\frac{-22}{-440}
=1/20
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+11}{2*-220}=\frac{0}{-440}
=0
$