7-2x^2=-47

Solution for 7-2x^2=-47 equation:

7-2x^2=-47

We move all terms to the left:

7-2x^2-(-47)=0

We add all the numbers together, and all the variables

-2x^2+54=0

a = -2; b = 0; c = +54;
Δ = b2-4ac
Δ = 02-4·(-2)·54
Δ = 432
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:

$\sqrt{\Delta}=\sqrt{432}=\sqrt{144*3}=\sqrt{144}*\sqrt{3}=12\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-12\sqrt{3}}{2*-2}=\frac{0-12\sqrt{3}}{-4}
=-\frac{12\sqrt{3}}{-4}
=-\frac{3\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+12\sqrt{3}}{2*-2}=\frac{0+12\sqrt{3}}{-4}
=\frac{12\sqrt{3}}{-4}
=\frac{3\sqrt{3}}{-1}
$