41/3b+b=6b-10.

Solution for 41/3b+b=6b-10. equation:

41/3b+b=6b-10.

We move all terms to the left:

41/3b+b-(6b-10.)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

41/3b+b-(6b-10)=0

We add all the numbers together, and all the variables

b+41/3b-(6b-10)=0

We get rid of parentheses

b+41/3b-6b+10=0

We multiply all the terms by the denominator


b*3b-6b*3b+10*3b+41=0

Wy multiply elements

3b^2-18b^2+30b+41=0

We add all the numbers together, and all the variables

-15b^2+30b+41=0

a = -15; b = 30; c = +41;
Δ = b2-4ac
Δ = 302-4·(-15)·41
Δ = 3360
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{3360}=\sqrt{16*210}=\sqrt{16}*\sqrt{210}=4\sqrt{210}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-4\sqrt{210}}{2*-15}=\frac{-30-4\sqrt{210}}{-30}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+4\sqrt{210}}{2*-15}=\frac{-30+4\sqrt{210}}{-30}
$