9-10r-r^2=0

Solution for 9-10r-r^2=0 equation:

9-10r-r^2=0

We add all the numbers together, and all the variables

-1r^2-10r+9=0

a = -1; b = -10; c = +9;
Δ = b2-4ac
Δ = -102-4·(-1)·9
Δ = 136
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$r_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{34}}{2*-1}=\frac{10-2\sqrt{34}}{-2}
$
$r_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{34}}{2*-1}=\frac{10+2\sqrt{34}}{-2}
$