F(x)=2x2+6x+-8

Solution for F(x)=2x2+6x+-8 equation:

(F)=2F^2+6F+-8

We move all terms to the left:

(F)-(2F^2+6F+-8)=0

We use the square of the difference formula

F-(2F^2+6F-8)=0

We get rid of parentheses

-2F^2+F-6F+8=0

We add all the numbers together, and all the variables

-2F^2-5F+8=0

a = -2; b = -5; c = +8;
Δ = b2-4ac
Δ = -52-4·(-2)·8
Δ = 89
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{89}}{2*-2}=\frac{5-\sqrt{89}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-5)+\sqrt{89}}{2*-2}=\frac{5+\sqrt{89}}{-4}
$