b-43=9-b2

Solution for b-43=9-b2 equation:

b-43=9-b2

We move all terms to the left:

b-43-(9-b2)=0

We add all the numbers together, and all the variables

-(-1b^2+9)+b-43=0

We get rid of parentheses

1b^2+b-9-43=0

We add all the numbers together, and all the variables

b^2+b-52=0

a = 1; b = 1; c = -52;
Δ = b2-4ac
Δ = 12-4·1·(-52)
Δ = 209
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-\sqrt{209}}{2*1}=\frac{-1-\sqrt{209}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{209}}{2*1}=\frac{-1+\sqrt{209}}{2}
$