488-x^2-10x=0

Solution for 488-x^2-10x=0 equation:

488-x^2-10x=0

We add all the numbers together, and all the variables

-1x^2-10x+488=0

a = -1; b = -10; c = +488;
Δ = b2-4ac
Δ = -102-4·(-1)·488
Δ = 2052
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:

$\sqrt{\Delta}=\sqrt{2052}=\sqrt{36*57}=\sqrt{36}*\sqrt{57}=6\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-6\sqrt{57}}{2*-1}=\frac{10-6\sqrt{57}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+6\sqrt{57}}{2*-1}=\frac{10+6\sqrt{57}}{-2}
$