0=b^2+35b+34

Solution for 0=b^2+35b+34 equation:

0=b^2+35b+34

We move all terms to the left:

0-(b^2+35b+34)=0

We add all the numbers together, and all the variables

-(b^2+35b+34)=0

We get rid of parentheses

-b^2-35b-34=0

We add all the numbers together, and all the variables

-1b^2-35b-34=0

a = -1; b = -35; c = -34;
Δ = b2-4ac
Δ = -352-4·(-1)·(-34)
Δ = 1089
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1089}=33$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-35)-33}{2*-1}=\frac{2}{-2}
=-1
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-35)+33}{2*-1}=\frac{68}{-2}
=-34
$