10x2=+5

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Solution for 10x2=+5 equation:



10x^2=+5
We move all terms to the left:
10x^2-(+5)=0
We add all the numbers together, and all the variables
10x^2-5=0
a = 10; b = 0; c = -5;
Δ = b2-4ac
Δ = 02-4·10·(-5)
Δ = 200
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:
$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-10\sqrt{2}}{2*10}=\frac{0-10\sqrt{2}}{20} =-\frac{10\sqrt{2}}{20} =-\frac{\sqrt{2}}{2} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*10}=\frac{0+10\sqrt{2}}{20} =\frac{10\sqrt{2}}{20} =\frac{\sqrt{2}}{2} $

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