5b(6+b)-3=82

Solution for 5b(6+b)-3=82 equation:

5b(6+b)-3=82

We move all terms to the left:

5b(6+b)-3-(82)=0

We add all the numbers together, and all the variables

5b(b+6)-3-82=0

We add all the numbers together, and all the variables

5b(b+6)-85=0

We multiply parentheses

5b^2+30b-85=0

a = 5; b = 30; c = -85;
Δ = b2-4ac
Δ = 302-4·5·(-85)
Δ = 2600
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:

$\sqrt{\Delta}=\sqrt{2600}=\sqrt{100*26}=\sqrt{100}*\sqrt{26}=10\sqrt{26}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(30)-10\sqrt{26}}{2*5}=\frac{-30-10\sqrt{26}}{10}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(30)+10\sqrt{26}}{2*5}=\frac{-30+10\sqrt{26}}{10}
$