10+14x2=48

Solution for 10+14x2=48 equation:

10+14x^2=48

We move all terms to the left:

10+14x^2-(48)=0

We add all the numbers together, and all the variables

14x^2-38=0

a = 14; b = 0; c = -38;
Δ = b2-4ac
Δ = 02-4·14·(-38)
Δ = 2128
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:

$\sqrt{\Delta}=\sqrt{2128}=\sqrt{16*133}=\sqrt{16}*\sqrt{133}=4\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-4\sqrt{133}}{2*14}=\frac{0-4\sqrt{133}}{28}
=-\frac{4\sqrt{133}}{28}
=-\frac{\sqrt{133}}{7}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+4\sqrt{133}}{2*14}=\frac{0+4\sqrt{133}}{28}
=\frac{4\sqrt{133}}{28}
=\frac{\sqrt{133}}{7}
$