b^2+1/16=36

Solution for b^2+1/16=36 equation:

b^2+1/16=36

We move all terms to the left:

b^2+1/16-(36)=0

determiningTheFunctionDomain
b^2-36+1/16=0

We multiply all the terms by the denominator


b^2*16+1-36*16=0

We add all the numbers together, and all the variables

b^2*16-575=0

Wy multiply elements

16b^2-575=0

a = 16; b = 0; c = -575;
Δ = b2-4ac
Δ = 02-4·16·(-575)
Δ = 36800
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{36800}=\sqrt{1600*23}=\sqrt{1600}*\sqrt{23}=40\sqrt{23}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{23}}{2*16}=\frac{0-40\sqrt{23}}{32}
=-\frac{40\sqrt{23}}{32}
=-\frac{5\sqrt{23}}{4}
$
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{23}}{2*16}=\frac{0+40\sqrt{23}}{32}
=\frac{40\sqrt{23}}{32}
=\frac{5\sqrt{23}}{4}
$