8x2+5=285

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Solution for 8x2+5=285 equation:



8x^2+5=285
We move all terms to the left:
8x^2+5-(285)=0
We add all the numbers together, and all the variables
8x^2-280=0
a = 8; b = 0; c = -280;
Δ = b2-4ac
Δ = 02-4·8·(-280)
Δ = 8960
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:
$\sqrt{\Delta}=\sqrt{8960}=\sqrt{256*35}=\sqrt{256}*\sqrt{35}=16\sqrt{35}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-16\sqrt{35}}{2*8}=\frac{0-16\sqrt{35}}{16} =-\frac{16\sqrt{35}}{16} =-\sqrt{35} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+16\sqrt{35}}{2*8}=\frac{0+16\sqrt{35}}{16} =\frac{16\sqrt{35}}{16} =\sqrt{35} $

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