x=x2-15x-10

Solution for x=x2-15x-10 equation:

x=x2-15x-10

We move all terms to the left:

x-(x2-15x-10)=0

We add all the numbers together, and all the variables

-(+x^2-15x-10)+x=0

We get rid of parentheses

-x^2+15x+x+10=0

We add all the numbers together, and all the variables

-1x^2+16x+10=0

a = -1; b = 16; c = +10;
Δ = b2-4ac
Δ = 162-4·(-1)·10
Δ = 296
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:

$\sqrt{\Delta}=\sqrt{296}=\sqrt{4*74}=\sqrt{4}*\sqrt{74}=2\sqrt{74}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{74}}{2*-1}=\frac{-16-2\sqrt{74}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{74}}{2*-1}=\frac{-16+2\sqrt{74}}{-2}
$