F(x)=x2-26x+144

Solution for F(x)=x2-26x+144 equation:

(F)=F2-26F+144

We move all terms to the left:

(F)-(F2-26F+144)=0

We add all the numbers together, and all the variables

-(+F^2-26F+144)+F=0

We get rid of parentheses

-F^2+26F+F-144=0

We add all the numbers together, and all the variables

-1F^2+27F-144=0

a = -1; b = 27; c = -144;
Δ = b2-4ac
Δ = 272-4·(-1)·(-144)
Δ = 153
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{153}=\sqrt{9*17}=\sqrt{9}*\sqrt{17}=3\sqrt{17}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(27)-3\sqrt{17}}{2*-1}=\frac{-27-3\sqrt{17}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(27)+3\sqrt{17}}{2*-1}=\frac{-27+3\sqrt{17}}{-2}
$