3b^2-6=-7b

Solution for 3b^2-6=-7b equation:

3b^2-6=-7b

We move all terms to the left:

3b^2-6-(-7b)=0

We get rid of parentheses

3b^2+7b-6=0

a = 3; b = 7; c = -6;
Δ = b2-4ac
Δ = 72-4·3·(-6)
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-11}{2*3}=\frac{-18}{6}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+11}{2*3}=\frac{4}{6}
=2/3
$