F(x)=5x2+-8

Solution for F(x)=5x2+-8 equation:

(F)=5F^2+-8

We move all terms to the left:

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

We use the square of the difference formula

F-(5F^2-8)=0

We get rid of parentheses

-5F^2+F+8=0

a = -5; b = 1; c = +8;
Δ = b2-4ac
Δ = 12-4·(-5)·8
Δ = 161
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{-(1)-\sqrt{161}}{2*-5}=\frac{-1-\sqrt{161}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(1)+\sqrt{161}}{2*-5}=\frac{-1+\sqrt{161}}{-10}
$