(6b-7)(b+6)=0

Solution for (6b-7)(b+6)=0 equation:

(6b-7)(b+6)=0

We multiply parentheses ..

(+6b^2+36b-7b-42)=0

We get rid of parentheses

6b^2+36b-7b-42=0

We add all the numbers together, and all the variables

6b^2+29b-42=0

a = 6; b = 29; c = -42;
Δ = b2-4ac
Δ = 292-4·6·(-42)
Δ = 1849
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1849}=43$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(29)-43}{2*6}=\frac{-72}{12}
=-6
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(29)+43}{2*6}=\frac{14}{12}
=1+1/6
$