0=x^2-38x+10

Solution for 0=x^2-38x+10 equation:

0=x^2-38x+10

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We get rid of parentheses

-x^2+38x-10=0

We add all the numbers together, and all the variables

-1x^2+38x-10=0

a = -1; b = 38; c = -10;
Δ = b2-4ac
Δ = 382-4·(-1)·(-10)
Δ = 1404
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:

$\sqrt{\Delta}=\sqrt{1404}=\sqrt{36*39}=\sqrt{36}*\sqrt{39}=6\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(38)-6\sqrt{39}}{2*-1}=\frac{-38-6\sqrt{39}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(38)+6\sqrt{39}}{2*-1}=\frac{-38+6\sqrt{39}}{-2}
$