8b^2+11b-42=-5b

Solution for 8b^2+11b-42=-5b equation:

8b^2+11b-42=-5b

We move all terms to the left:

8b^2+11b-42-(-5b)=0

We get rid of parentheses

8b^2+11b+5b-42=0

We add all the numbers together, and all the variables

8b^2+16b-42=0

a = 8; b = 16; c = -42;
Δ = b2-4ac
Δ = 162-4·8·(-42)
Δ = 1600
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1600}=40$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-40}{2*8}=\frac{-56}{16}
=-3+1/2
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+40}{2*8}=\frac{24}{16}
=1+1/2
$