F(x)=2x^2+6x+-5

Solution for F(x)=2x^2+6x+-5 equation:

(F)=2F^2+6F+-5

We move all terms to the left:

(F)-(2F^2+6F+-5)=0

We use the square of the difference formula

F-(2F^2+6F-5)=0

We get rid of parentheses

-2F^2+F-6F+5=0

We add all the numbers together, and all the variables

-2F^2-5F+5=0

a = -2; b = -5; c = +5;
Δ = b2-4ac
Δ = -52-4·(-2)·5
Δ = 65
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{-(-5)-\sqrt{65}}{2*-2}=\frac{5-\sqrt{65}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{65}}{2*-2}=\frac{5+\sqrt{65}}{-4}
$