19.6^2+b^2=89.5^2

Solution for 19.6^2+b^2=89.5^2 equation:

19.6^2+b^2=89.5^2

We move all terms to the left:

19.6^2+b^2-(89.5^2)=0

We add all the numbers together, and all the variables

b^2-7626.09=0

a = 1; b = 0; c = -7626.09;
Δ = b2-4ac
Δ = 02-4·1·(-7626.09)
Δ = 30504.36
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-\sqrt{30504.36}}{2*1}=\frac{0-\sqrt{30504.36}}{2}
=-\frac{\sqrt{}}{2}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+\sqrt{30504.36}}{2*1}=\frac{0+\sqrt{30504.36}}{2}
=\frac{\sqrt{}}{2}
$