2b^2=39+7b

Solution for 2b^2=39+7b equation:

2b^2=39+7b

We move all terms to the left:

2b^2-(39+7b)=0

We add all the numbers together, and all the variables

2b^2-(7b+39)=0

We get rid of parentheses

2b^2-7b-39=0

a = 2; b = -7; c = -39;
Δ = b2-4ac
Δ = -72-4·2·(-39)
Δ = 361
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{361}=19$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-19}{2*2}=\frac{-12}{4}
=-3
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+19}{2*2}=\frac{26}{4}
=6+1/2
$