4b+1/3b+b=6b-10.4

Solution for 4b+1/3b+b=6b-10.4 equation:

4b+1/3b+b=6b-10.4

We move all terms to the left:

4b+1/3b+b-(6b-10.4)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

5b+1/3b-(6b-10.4)=0

We get rid of parentheses

5b+1/3b-6b+10.4=0

We multiply all the terms by the denominator


5b*3b-6b*3b+(10.4)*3b+1=0

We multiply parentheses

5b*3b-6b*3b+31.2b+1=0

Wy multiply elements

15b^2-18b^2+31.2b+1=0

We add all the numbers together, and all the variables

-3b^2+31.2b+1=0

a = -3; b = 31.2; c = +1;
Δ = b2-4ac
Δ = 31.22-4·(-3)·1
Δ = 985.44
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(31.2)-\sqrt{985.44}}{2*-3}=\frac{-31.2-\sqrt{985.44}}{-6}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31.2)+\sqrt{985.44}}{2*-3}=\frac{-31.2+\sqrt{985.44}}{-6}
$