26x-x^2=144

Solution for 26x-x^2=144 equation:

26x-x^2=144

We move all terms to the left:

26x-x^2-(144)=0

We add all the numbers together, and all the variables

-1x^2+26x-144=0

a = -1; b = 26; c = -144;
Δ = b2-4ac
Δ = 262-4·(-1)·(-144)
Δ = 100
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{100}=10$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(26)-10}{2*-1}=\frac{-36}{-2}
=+18
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(26)+10}{2*-1}=\frac{-16}{-2}
=+8
$