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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-2F^2+7F=0

a = -2; b = 7; c = 0;
Δ = b2-4ac
Δ = 72-4·(-2)·0
Δ = 49
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{49}=7$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(7)-7}{2*-2}=\frac{-14}{-4}
=3+1/2
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+7}{2*-2}=\frac{0}{-4}
=0
$