F(x)=(2x-11)(2x-1)=-25

Solution for F(x)=(2x-11)(2x-1)=-25 equation:

(F)=(2F-11)(2F-1)=-25

We move all terms to the left:

(F)-((2F-11)(2F-1))=0

We multiply parentheses ..

-((+4F^2-2F-22F+11))+F=0


We calculate terms in parentheses: -((+4F^2-2F-22F+11)), so:

(+4F^2-2F-22F+11)

We get rid of parentheses

4F^2-2F-22F+11

We add all the numbers together, and all the variables

4F^2-24F+11

Back to the equation:

-(4F^2-24F+11)


We add all the numbers together, and all the variables

F-(4F^2-24F+11)=0

We get rid of parentheses

-4F^2+F+24F-11=0

We add all the numbers together, and all the variables

-4F^2+25F-11=0

a = -4; b = 25; c = -11;
Δ = b2-4ac
Δ = 252-4·(-4)·(-11)
Δ = 449
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(25)-\sqrt{449}}{2*-4}=\frac{-25-\sqrt{449}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(25)+\sqrt{449}}{2*-4}=\frac{-25+\sqrt{449}}{-8}
$