7b^2=-42+49b

Solution for 7b^2=-42+49b equation:

7b^2=-42+49b

We move all terms to the left:

7b^2-(-42+49b)=0

We add all the numbers together, and all the variables

7b^2-(49b-42)=0

We get rid of parentheses

7b^2-49b+42=0

a = 7; b = -49; c = +42;
Δ = b2-4ac
Δ = -492-4·7·42
Δ = 1225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1225}=35$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-49)-35}{2*7}=\frac{14}{14}
=1
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-49)+35}{2*7}=\frac{84}{14}
=6
$