6b-3(b+7)-(5-4b)b=2

Solution for 6b-3(b+7)-(5-4b)b=2 equation:

6b-3(b+7)-(5-4b)b=2

We move all terms to the left:

6b-3(b+7)-(5-4b)b-(2)=0

We add all the numbers together, and all the variables

6b-3(b+7)-(-4b+5)b-2=0

We multiply parentheses

4b^2+6b-3b-5b-21-2=0

We add all the numbers together, and all the variables

4b^2-2b-23=0

a = 4; b = -2; c = -23;
Δ = b2-4ac
Δ = -22-4·4·(-23)
Δ = 372
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:

$\sqrt{\Delta}=\sqrt{372}=\sqrt{4*93}=\sqrt{4}*\sqrt{93}=2\sqrt{93}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{93}}{2*4}=\frac{2-2\sqrt{93}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{93}}{2*4}=\frac{2+2\sqrt{93}}{8}
$