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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -2; b = 15; c = -15;
Δ = b2-4ac
Δ = 152-4·(-2)·(-15)
Δ = 105
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{-(15)-\sqrt{105}}{2*-2}=\frac{-15-\sqrt{105}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(15)+\sqrt{105}}{2*-2}=\frac{-15+\sqrt{105}}{-4}
$