4b(5+b)=6

Solution for 4b(5+b)=6 equation:

4b(5+b)=6

We move all terms to the left:

4b(5+b)-(6)=0

We add all the numbers together, and all the variables

4b(b+5)-6=0

We multiply parentheses

4b^2+20b-6=0

a = 4; b = 20; c = -6;
Δ = b2-4ac
Δ = 202-4·4·(-6)
Δ = 496
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:

$\sqrt{\Delta}=\sqrt{496}=\sqrt{16*31}=\sqrt{16}*\sqrt{31}=4\sqrt{31}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(20)-4\sqrt{31}}{2*4}=\frac{-20-4\sqrt{31}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+4\sqrt{31}}{2*4}=\frac{-20+4\sqrt{31}}{8}
$