24x-x^2=110

Solution for 24x-x^2=110 equation:

24x-x^2=110

We move all terms to the left:

24x-x^2-(110)=0

We add all the numbers together, and all the variables

-1x^2+24x-110=0

a = -1; b = 24; c = -110;
Δ = b2-4ac
Δ = 242-4·(-1)·(-110)
Δ = 136
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:

$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(24)-2\sqrt{34}}{2*-1}=\frac{-24-2\sqrt{34}}{-2}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(24)+2\sqrt{34}}{2*-1}=\frac{-24+2\sqrt{34}}{-2}
$