5b^2-42b=-49

Solution for 5b^2-42b=-49 equation:

5b^2-42b=-49

We move all terms to the left:

5b^2-42b-(-49)=0

We add all the numbers together, and all the variables

5b^2-42b+49=0

a = 5; b = -42; c = +49;
Δ = b2-4ac
Δ = -422-4·5·49
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-28}{2*5}=\frac{14}{10}
=1+2/5
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+28}{2*5}=\frac{70}{10}
=7
$