F(x)=3x^2-30x+72

Solution for F(x)=3x^2-30x+72 equation:

(F)=3F^2-30F+72

We move all terms to the left:

(F)-(3F^2-30F+72)=0

We get rid of parentheses

-3F^2+F+30F-72=0

We add all the numbers together, and all the variables

-3F^2+31F-72=0

a = -3; b = 31; c = -72;
Δ = b2-4ac
Δ = 312-4·(-3)·(-72)
Δ = 97
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{-(31)-\sqrt{97}}{2*-3}=\frac{-31-\sqrt{97}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(31)+\sqrt{97}}{2*-3}=\frac{-31+\sqrt{97}}{-6}
$