x^2=14x-38=0

Solution for x^2=14x-38=0 equation:

x^2=14x-38=0

We move all terms to the left:

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

We get rid of parentheses

x^2-14x+38=0

a = 1; b = -14; c = +38;
Δ = b2-4ac
Δ = -142-4·1·38
Δ = 44
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:

$\sqrt{\Delta}=\sqrt{44}=\sqrt{4*11}=\sqrt{4}*\sqrt{11}=2\sqrt{11}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-2\sqrt{11}}{2*1}=\frac{14-2\sqrt{11}}{2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+2\sqrt{11}}{2*1}=\frac{14+2\sqrt{11}}{2}
$