2/5x2+7=12

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Solution for 2/5x2+7=12 equation:



2/5x^2+7=12
We move all terms to the left:
2/5x^2+7-(12)=0
Domain of the equation: 5x^2!=0
x^2!=0/5
x^2!=√0
x!=0
x∈R
We add all the numbers together, and all the variables
2/5x^2-5=0
We multiply all the terms by the denominator
-5*5x^2+2=0
Wy multiply elements
-25x^2+2=0
a = -25; b = 0; c = +2;
Δ = b2-4ac
Δ = 02-4·(-25)·2
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*-25}=\frac{0-10\sqrt{2}}{-50} =-\frac{10\sqrt{2}}{-50} =-\frac{\sqrt{2}}{-5} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*-25}=\frac{0+10\sqrt{2}}{-50} =\frac{10\sqrt{2}}{-50} =\frac{\sqrt{2}}{-5} $

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