14x^2=126^2

Solution for 14x^2=126^2 equation:

14x^2=126^2

We move all terms to the left:

14x^2-(126^2)=0

We add all the numbers together, and all the variables

14x^2-15876=0

a = 14; b = 0; c = -15876;
Δ = b2-4ac
Δ = 02-4·14·(-15876)
Δ = 889056
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:

$\sqrt{\Delta}=\sqrt{889056}=\sqrt{63504*14}=\sqrt{63504}*\sqrt{14}=252\sqrt{14}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-252\sqrt{14}}{2*14}=\frac{0-252\sqrt{14}}{28}
=-\frac{252\sqrt{14}}{28}
=-9\sqrt{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+252\sqrt{14}}{2*14}=\frac{0+252\sqrt{14}}{28}
=\frac{252\sqrt{14}}{28}
=9\sqrt{14}
$