F(x)=2x2-6x+4

Solution for F(x)=2x2-6x+4 equation:

(F)=2F^2-6F+4

We move all terms to the left:

(F)-(2F^2-6F+4)=0

We get rid of parentheses

-2F^2+F+6F-4=0

We add all the numbers together, and all the variables

-2F^2+7F-4=0

a = -2; b = 7; c = -4;
Δ = b2-4ac
Δ = 72-4·(-2)·(-4)
Δ = 17
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{-(7)-\sqrt{17}}{2*-2}=\frac{-7-\sqrt{17}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{17}}{2*-2}=\frac{-7+\sqrt{17}}{-4}
$