8x2-18-24=0

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Solution for 8x2-18-24=0 equation:



8x^2-18-24=0
We add all the numbers together, and all the variables
8x^2-42=0
a = 8; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·8·(-42)
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*8}=\frac{0-8\sqrt{21}}{16} =-\frac{8\sqrt{21}}{16} =-\frac{\sqrt{21}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{21}}{2*8}=\frac{0+8\sqrt{21}}{16} =\frac{8\sqrt{21}}{16} =\frac{\sqrt{21}}{2} $

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