1/3b+15=2b+-25

Solution for 1/3b+15=2b+-25 equation:

1/3b+15=2b+-25

We move all terms to the left:

1/3b+15-(2b+-25)=0


Domain of the equation: 3b!=0

b!=0/3

b!=0

b∈R


We add all the numbers together, and all the variables

1/3b-(2b-25)+15=0

We get rid of parentheses

1/3b-2b+25+15=0

We multiply all the terms by the denominator


-2b*3b+25*3b+15*3b+1=0

Wy multiply elements

-6b^2+75b+45b+1=0

We add all the numbers together, and all the variables

-6b^2+120b+1=0

a = -6; b = 120; c = +1;
Δ = b2-4ac
Δ = 1202-4·(-6)·1
Δ = 14424
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:

$\sqrt{\Delta}=\sqrt{14424}=\sqrt{4*3606}=\sqrt{4}*\sqrt{3606}=2\sqrt{3606}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(120)-2\sqrt{3606}}{2*-6}=\frac{-120-2\sqrt{3606}}{-12}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(120)+2\sqrt{3606}}{2*-6}=\frac{-120+2\sqrt{3606}}{-12}
$