10+14x2=38

Solution for 10+14x2=38 equation:

10+14x^2=38

We move all terms to the left:

10+14x^2-(38)=0

We add all the numbers together, and all the variables

14x^2-28=0

a = 14; b = 0; c = -28;
Δ = b2-4ac
Δ = 02-4·14·(-28)
Δ = 1568
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:

$\sqrt{\Delta}=\sqrt{1568}=\sqrt{784*2}=\sqrt{784}*\sqrt{2}=28\sqrt{2}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-28\sqrt{2}}{2*14}=\frac{0-28\sqrt{2}}{28}
=-\frac{28\sqrt{2}}{28}
=-\sqrt{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+28\sqrt{2}}{2*14}=\frac{0+28\sqrt{2}}{28}
=\frac{28\sqrt{2}}{28}
=\sqrt{2}
$