6-1/2x^2=-19

Solution for 6-1/2x^2=-19 equation:

6-1/2x^2=-19

We move all terms to the left:

6-1/2x^2-(-19)=0


Domain of the equation: 2x^2!=0

x^2!=0/2

x^2!=√0

x!=0

x∈R


We add all the numbers together, and all the variables

-1/2x^2+25=0

We multiply all the terms by the denominator


25*2x^2-1=0

Wy multiply elements

50x^2-1=0

a = 50; b = 0; c = -1;
Δ = b2-4ac
Δ = 02-4·50·(-1)
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*50}=\frac{0-10\sqrt{2}}{100}
=-\frac{10\sqrt{2}}{100}
=-\frac{\sqrt{2}}{10}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+10\sqrt{2}}{2*50}=\frac{0+10\sqrt{2}}{100}
=\frac{10\sqrt{2}}{100}
=\frac{\sqrt{2}}{10}
$