5+11x2=47

Solution for 5+11x2=47 equation:

5+11x^2=47

We move all terms to the left:

5+11x^2-(47)=0

We add all the numbers together, and all the variables

11x^2-42=0

a = 11; b = 0; c = -42;
Δ = b2-4ac
Δ = 02-4·11·(-42)
Δ = 1848
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:

$\sqrt{\Delta}=\sqrt{1848}=\sqrt{4*462}=\sqrt{4}*\sqrt{462}=2\sqrt{462}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-2\sqrt{462}}{2*11}=\frac{0-2\sqrt{462}}{22}
=-\frac{2\sqrt{462}}{22}
=-\frac{\sqrt{462}}{11}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+2\sqrt{462}}{2*11}=\frac{0+2\sqrt{462}}{22}
=\frac{2\sqrt{462}}{22}
=\frac{\sqrt{462}}{11}
$