0=x^2+10x+6

Solution for 0=x^2+10x+6 equation:

0=x^2+10x+6

We move all terms to the left:

0-(x^2+10x+6)=0

We add all the numbers together, and all the variables

-(x^2+10x+6)=0

We get rid of parentheses

-x^2-10x-6=0

We add all the numbers together, and all the variables

-1x^2-10x-6=0

a = -1; b = -10; c = -6;
Δ = b2-4ac
Δ = -102-4·(-1)·(-6)
Δ = 76
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:

$\sqrt{\Delta}=\sqrt{76}=\sqrt{4*19}=\sqrt{4}*\sqrt{19}=2\sqrt{19}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{19}}{2*-1}=\frac{10-2\sqrt{19}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{19}}{2*-1}=\frac{10+2\sqrt{19}}{-2}
$