8b^2-41b-39=3

Solution for 8b^2-41b-39=3 equation:

8b^2-41b-39=3

We move all terms to the left:

8b^2-41b-39-(3)=0

We add all the numbers together, and all the variables

8b^2-41b-42=0

a = 8; b = -41; c = -42;
Δ = b2-4ac
Δ = -412-4·8·(-42)
Δ = 3025
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{3025}=55$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-41)-55}{2*8}=\frac{-14}{16}
=-7/8
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-41)+55}{2*8}=\frac{96}{16}
=6
$