14x^2-5=11

Solution for 14x^2-5=11 equation:

14x^2-5=11

We move all terms to the left:

14x^2-5-(11)=0

We add all the numbers together, and all the variables

14x^2-16=0

a = 14; b = 0; c = -16;
Δ = b2-4ac
Δ = 02-4·14·(-16)
Δ = 896
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:

$\sqrt{\Delta}=\sqrt{896}=\sqrt{64*14}=\sqrt{64}*\sqrt{14}=8\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-8\sqrt{14}}{2*14}=\frac{0-8\sqrt{14}}{28}
=-\frac{8\sqrt{14}}{28}
=-\frac{2\sqrt{14}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+8\sqrt{14}}{2*14}=\frac{0+8\sqrt{14}}{28}
=\frac{8\sqrt{14}}{28}
=\frac{2\sqrt{14}}{7}
$