14x^2=24+54

Solution for 14x^2=24+54 equation:

14x^2=24+54

We move all terms to the left:

14x^2-(24+54)=0

We add all the numbers together, and all the variables

14x^2-78=0

a = 14; b = 0; c = -78;
Δ = b2-4ac
Δ = 02-4·14·(-78)
Δ = 4368
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:

$\sqrt{\Delta}=\sqrt{4368}=\sqrt{16*273}=\sqrt{16}*\sqrt{273}=4\sqrt{273}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{273}}{2*14}=\frac{0-4\sqrt{273}}{28}
=-\frac{4\sqrt{273}}{28}
=-\frac{\sqrt{273}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{273}}{2*14}=\frac{0+4\sqrt{273}}{28}
=\frac{4\sqrt{273}}{28}
=\frac{\sqrt{273}}{7}
$