F(x)=4x^2-15x+14

Solution for F(x)=4x^2-15x+14 equation:

(F)=4F^2-15F+14

We move all terms to the left:

(F)-(4F^2-15F+14)=0

We get rid of parentheses

-4F^2+F+15F-14=0

We add all the numbers together, and all the variables

-4F^2+16F-14=0

a = -4; b = 16; c = -14;
Δ = b2-4ac
Δ = 162-4·(-4)·(-14)
Δ = 32
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{32}=\sqrt{16*2}=\sqrt{16}*\sqrt{2}=4\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-4\sqrt{2}}{2*-4}=\frac{-16-4\sqrt{2}}{-8}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+4\sqrt{2}}{2*-4}=\frac{-16+4\sqrt{2}}{-8}
$