F(x)=5x^2-8x-3

Solution for F(x)=5x^2-8x-3 equation:

(F)=5F^2-8F-3

We move all terms to the left:

(F)-(5F^2-8F-3)=0

We get rid of parentheses

-5F^2+F+8F+3=0

We add all the numbers together, and all the variables

-5F^2+9F+3=0

a = -5; b = 9; c = +3;
Δ = b2-4ac
Δ = 92-4·(-5)·3
Δ = 141
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{-(9)-\sqrt{141}}{2*-5}=\frac{-9-\sqrt{141}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9)+\sqrt{141}}{2*-5}=\frac{-9+\sqrt{141}}{-10}
$