4b^2-8b-35=9

Solution for 4b^2-8b-35=9 equation:

4b^2-8b-35=9

We move all terms to the left:

4b^2-8b-35-(9)=0

We add all the numbers together, and all the variables

4b^2-8b-44=0

a = 4; b = -8; c = -44;
Δ = b2-4ac
Δ = -82-4·4·(-44)
Δ = 768
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{768}=\sqrt{256*3}=\sqrt{256}*\sqrt{3}=16\sqrt{3}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-8)-16\sqrt{3}}{2*4}=\frac{8-16\sqrt{3}}{8}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-8)+16\sqrt{3}}{2*4}=\frac{8+16\sqrt{3}}{8}
$