2/5x2+7=12

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}
$