F(x)-x2=5x-22

Solution for F(x)-x2=5x-22 equation:

(F)-F2=5F-22

We move all terms to the left:

(F)-F2-(5F-22)=0

We add all the numbers together, and all the variables

-1F^2+F-(5F-22)=0

We get rid of parentheses

-1F^2+F-5F+22=0

We add all the numbers together, and all the variables

-1F^2-4F+22=0

a = -1; b = -4; c = +22;
Δ = b2-4ac
Δ = -42-4·(-1)·22
Δ = 104
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:

$\sqrt{\Delta}=\sqrt{104}=\sqrt{4*26}=\sqrt{4}*\sqrt{26}=2\sqrt{26}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{26}}{2*-1}=\frac{4-2\sqrt{26}}{-2}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{26}}{2*-1}=\frac{4+2\sqrt{26}}{-2}
$