4/5b-4=1/3b+84

Solution for 4/5b-4=1/3b+84 equation:

4/5b-4=1/3b+84

We move all terms to the left:

4/5b-4-(1/3b+84)=0


Domain of the equation: 5b!=0

b!=0/5

b!=0

b∈R



Domain of the equation: 3b+84)!=0

b∈R


We get rid of parentheses

4/5b-1/3b-84-4=0

We calculate fractions


12b/15b^2+(-5b)/15b^2-84-4=0

We add all the numbers together, and all the variables

12b/15b^2+(-5b)/15b^2-88=0

We multiply all the terms by the denominator


12b+(-5b)-88*15b^2=0

Wy multiply elements

-1320b^2+12b+(-5b)=0

We get rid of parentheses

-1320b^2+12b-5b=0

We add all the numbers together, and all the variables

-1320b^2+7b=0

a = -1320; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-1320)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-1320}=\frac{-14}{-2640}
=7/1320
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-1320}=\frac{0}{-2640}
=0
$