(6b+5)(b-1)=-3

Solution for (6b+5)(b-1)=-3 equation:

(6b+5)(b-1)=-3

We move all terms to the left:

(6b+5)(b-1)-(-3)=0

We add all the numbers together, and all the variables

(6b+5)(b-1)+3=0

We multiply parentheses ..

(+6b^2-6b+5b-5)+3=0

We get rid of parentheses

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

We add all the numbers together, and all the variables

6b^2-1b-2=0

a = 6; b = -1; c = -2;
Δ = b2-4ac
Δ = -12-4·6·(-2)
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-7}{2*6}=\frac{-6}{12}
=-1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+7}{2*6}=\frac{8}{12}
=2/3
$