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4x^2+16=100
We move all terms to the left:
4x^2+16-(100)=0
We add all the numbers together, and all the variables
4x^2-84=0
a = 4; b = 0; c = -84;
Δ = b2-4ac
Δ = 02-4·4·(-84)
Δ = 1344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{1344}=\sqrt{64*21}=\sqrt{64}*\sqrt{21}=8\sqrt{21}$$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{21}}{2*4}=\frac{0-8\sqrt{21}}{8} =-\frac{8\sqrt{21}}{8} =-\sqrt{21} $$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{21}}{2*4}=\frac{0+8\sqrt{21}}{8} =\frac{8\sqrt{21}}{8} =\sqrt{21} $
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