F(x)=4x^2-10x+3

Solution for F(x)=4x^2-10x+3 equation:

(F)=4F^2-10F+3

We move all terms to the left:

(F)-(4F^2-10F+3)=0

We get rid of parentheses

-4F^2+F+10F-3=0

We add all the numbers together, and all the variables

-4F^2+11F-3=0

a = -4; b = 11; c = -3;
Δ = b2-4ac
Δ = 112-4·(-4)·(-3)
Δ = 73
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{-(11)-\sqrt{73}}{2*-4}=\frac{-11-\sqrt{73}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(11)+\sqrt{73}}{2*-4}=\frac{-11+\sqrt{73}}{-8}
$