10x-x^2+180=0

Solution for 10x-x^2+180=0 equation:

10x-x^2+180=0

We add all the numbers together, and all the variables

-1x^2+10x+180=0

a = -1; b = 10; c = +180;
Δ = b2-4ac
Δ = 102-4·(-1)·180
Δ = 820
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:

$\sqrt{\Delta}=\sqrt{820}=\sqrt{4*205}=\sqrt{4}*\sqrt{205}=2\sqrt{205}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(10)-2\sqrt{205}}{2*-1}=\frac{-10-2\sqrt{205}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+2\sqrt{205}}{2*-1}=\frac{-10+2\sqrt{205}}{-2}
$