81+b2=256

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Solution for 81+b2=256 equation:



81+b2=256
We move all terms to the left:
81+b2-(256)=0
We add all the numbers together, and all the variables
b^2-175=0
a = 1; b = 0; c = -175;
Δ = b2-4ac
Δ = 02-4·1·(-175)
Δ = 700
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:
$\sqrt{\Delta}=\sqrt{700}=\sqrt{100*7}=\sqrt{100}*\sqrt{7}=10\sqrt{7}$
$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{7}}{2*1}=\frac{0-10\sqrt{7}}{2} =-\frac{10\sqrt{7}}{2} =-5\sqrt{7} $
$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{7}}{2*1}=\frac{0+10\sqrt{7}}{2} =\frac{10\sqrt{7}}{2} =5\sqrt{7} $

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