10x2+2=82

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Solution for 10x2+2=82 equation:



10x^2+2=82
We move all terms to the left:
10x^2+2-(82)=0
We add all the numbers together, and all the variables
10x^2-80=0
a = 10; b = 0; c = -80;
Δ = b2-4ac
Δ = 02-4·10·(-80)
Δ = 3200
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:
$\sqrt{\Delta}=\sqrt{3200}=\sqrt{1600*2}=\sqrt{1600}*\sqrt{2}=40\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-40\sqrt{2}}{2*10}=\frac{0-40\sqrt{2}}{20} =-\frac{40\sqrt{2}}{20} =-2\sqrt{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+40\sqrt{2}}{2*10}=\frac{0+40\sqrt{2}}{20} =\frac{40\sqrt{2}}{20} =2\sqrt{2} $

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