6b^2-9b=-106b

Solution for 6b^2-9b=-106b equation:

6b^2-9b=-106b

We move all terms to the left:

6b^2-9b-(-106b)=0

We get rid of parentheses

6b^2-9b+106b=0

We add all the numbers together, and all the variables

6b^2+97b=0

a = 6; b = 97; c = 0;
Δ = b2-4ac
Δ = 972-4·6·0
Δ = 9409
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9409}=97$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(97)-97}{2*6}=\frac{-194}{12}
=-16+1/6
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(97)+97}{2*6}=\frac{0}{12}
=0
$