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

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

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

We move all terms to the left:

4+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

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

We get rid of parentheses

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

We multiply all the terms by the denominator


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

We multiply parentheses

b*3b-6b*3b+31.2b+4*3b+1=0

Wy multiply elements

3b^2-18b^2+31.2b+12b+1=0

We add all the numbers together, and all the variables

-15b^2+43.2b+1=0

a = -15; b = 43.2; c = +1;
Δ = b2-4ac
Δ = 43.22-4·(-15)·1
Δ = 1926.24
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{-(43.2)-\sqrt{1926.24}}{2*-15}=\frac{-43.2-\sqrt{1926.24}}{-30}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(43.2)+\sqrt{1926.24}}{2*-15}=\frac{-43.2+\sqrt{1926.24}}{-30}
$