0=x^2+6x-38

Solution for 0=x^2+6x-38 equation:

0=x^2+6x-38

We move all terms to the left:

0-(x^2+6x-38)=0

We add all the numbers together, and all the variables

-(x^2+6x-38)=0

We get rid of parentheses

-x^2-6x+38=0

We add all the numbers together, and all the variables

-1x^2-6x+38=0

a = -1; b = -6; c = +38;
Δ = b2-4ac
Δ = -62-4·(-1)·38
Δ = 188
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:

$\sqrt{\Delta}=\sqrt{188}=\sqrt{4*47}=\sqrt{4}*\sqrt{47}=2\sqrt{47}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-6)-2\sqrt{47}}{2*-1}=\frac{6-2\sqrt{47}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-6)+2\sqrt{47}}{2*-1}=\frac{6+2\sqrt{47}}{-2}
$