F(x)=2x^2-15x+7

Solution for F(x)=2x^2-15x+7 equation:

(F)=2F^2-15F+7

We move all terms to the left:

(F)-(2F^2-15F+7)=0

We get rid of parentheses

-2F^2+F+15F-7=0

We add all the numbers together, and all the variables

-2F^2+16F-7=0

a = -2; b = 16; c = -7;
Δ = b2-4ac
Δ = 162-4·(-2)·(-7)
Δ = 200
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:

$\sqrt{\Delta}=\sqrt{200}=\sqrt{100*2}=\sqrt{100}*\sqrt{2}=10\sqrt{2}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-10\sqrt{2}}{2*-2}=\frac{-16-10\sqrt{2}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+10\sqrt{2}}{2*-2}=\frac{-16+10\sqrt{2}}{-4}
$