11x^2=47-14

Solution for 11x^2=47-14 equation:

11x^2=47-14

We move all terms to the left:

11x^2-(47-14)=0

We add all the numbers together, and all the variables

11x^2-33=0

a = 11; b = 0; c = -33;
Δ = b2-4ac
Δ = 02-4·11·(-33)
Δ = 1452
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:

$\sqrt{\Delta}=\sqrt{1452}=\sqrt{484*3}=\sqrt{484}*\sqrt{3}=22\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-22\sqrt{3}}{2*11}=\frac{0-22\sqrt{3}}{22}
=-\frac{22\sqrt{3}}{22}
=-\sqrt{3}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+22\sqrt{3}}{2*11}=\frac{0+22\sqrt{3}}{22}
=\frac{22\sqrt{3}}{22}
=\sqrt{3}
$