10x-x*x=6

Solution for 10x-x*x=6 equation:

10x-x*x=6

We move all terms to the left:

10x-x*x-(6)=0

Wy multiply elements

-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}
$