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

Solution for (x)=x^2+10x+6 equation:

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-1x^2-9x-6=0

a = -1; b = -9; c = -6;
Δ = b2-4ac
Δ = -92-4·(-1)·(-6)
Δ = 57
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-9)-\sqrt{57}}{2*-1}=\frac{9-\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-9)+\sqrt{57}}{2*-1}=\frac{9+\sqrt{57}}{-2}
$