32x2=7

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Solution for 32x2=7 equation:



32x^2=7
We move all terms to the left:
32x^2-(7)=0
a = 32; b = 0; c = -7;
Δ = b2-4ac
Δ = 02-4·32·(-7)
Δ = 896
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:
$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*32}=\frac{0-8\sqrt{14}}{64} =-\frac{8\sqrt{14}}{64} =-\frac{\sqrt{14}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*32}=\frac{0+8\sqrt{14}}{64} =\frac{8\sqrt{14}}{64} =\frac{\sqrt{14}}{8} $

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