2b+b*(25+b)=3

Solution for 2b+b*(25+b)=3 equation:

2b+b*(25+b)=3

We move all terms to the left:

2b+b*(25+b)-(3)=0

We add all the numbers together, and all the variables

2b+b*(b+25)-3=0

We multiply parentheses

b^2+2b+25b-3=0

We add all the numbers together, and all the variables

b^2+27b-3=0

a = 1; b = 27; c = -3;
Δ = b2-4ac
Δ = 272-4·1·(-3)
Δ = 741
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{-(27)-\sqrt{741}}{2*1}=\frac{-27-\sqrt{741}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+\sqrt{741}}{2*1}=\frac{-27+\sqrt{741}}{2}
$