F(x)=(30-2x)(30-2x)

Solution for F(x)=(30-2x)(30-2x) equation:

(F)=(30-2F)(30-2F)

We move all terms to the left:

(F)-((30-2F)(30-2F))=0

We add all the numbers together, and all the variables

F-((-2F+30)(-2F+30))=0

We multiply parentheses ..

-((+4F^2-60F-60F+900))+F=0


We calculate terms in parentheses: -((+4F^2-60F-60F+900)), so:

(+4F^2-60F-60F+900)

We get rid of parentheses

4F^2-60F-60F+900

We add all the numbers together, and all the variables

4F^2-120F+900

Back to the equation:

-(4F^2-120F+900)


We add all the numbers together, and all the variables

F-(4F^2-120F+900)=0

We get rid of parentheses

-4F^2+F+120F-900=0

We add all the numbers together, and all the variables

-4F^2+121F-900=0

a = -4; b = 121; c = -900;
Δ = b2-4ac
Δ = 1212-4·(-4)·(-900)
Δ = 241
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{-(121)-\sqrt{241}}{2*-4}=\frac{-121-\sqrt{241}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(121)+\sqrt{241}}{2*-4}=\frac{-121+\sqrt{241}}{-8}
$