9b^2-b=1+7b^2

Solution for 9b^2-b=1+7b^2 equation:

9b^2-b=1+7b^2

We move all terms to the left:

9b^2-b-(1+7b^2)=0

We add all the numbers together, and all the variables

9b^2-(1+7b^2)-1b=0

We get rid of parentheses

9b^2-7b^2-1b-1=0

We add all the numbers together, and all the variables

2b^2-1b-1=0

a = 2; b = -1; c = -1;
Δ = b2-4ac
Δ = -12-4·2·(-1)
Δ = 9
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{9}=3$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-1)-3}{2*2}=\frac{-2}{4}
=-1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-1)+3}{2*2}=\frac{4}{4}
=1
$