F(x)=x^2+3x^2=9x-27

Solution for F(x)=x^2+3x^2=9x-27 equation:

(F)=F^2+3F^2=9F-27

We move all terms to the left:

(F)-(F^2+3F^2)=0

We get rid of parentheses

-F^2-3F^2+F=0

We add all the numbers together, and all the variables

-4F^2+F=0

a = -4; b = 1; c = 0;
Δ = b2-4ac
Δ = 12-4·(-4)·0
Δ = 1
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{1}=1$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(1)-1}{2*-4}=\frac{-2}{-8}
=1/4
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+1}{2*-4}=\frac{0}{-8}
=0
$