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4b^2-5=2
We move all terms to the left:
4b^2-5-(2)=0
We add all the numbers together, and all the variables
4b^2-7=0
a = 4; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·4·(-7)
Δ = 112
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}$$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}$
The end solution:
$\sqrt{\Delta}=\sqrt{112}=\sqrt{16*7}=\sqrt{16}*\sqrt{7}=4\sqrt{7}$$b_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{7}}{2*4}=\frac{0-4\sqrt{7}}{8} =-\frac{4\sqrt{7}}{8} =-\frac{\sqrt{7}}{2} $$b_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{7}}{2*4}=\frac{0+4\sqrt{7}}{8} =\frac{4\sqrt{7}}{8} =\frac{\sqrt{7}}{2} $
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