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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

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

a = -5; b = -2; c = +8;
Δ = b2-4ac
Δ = -22-4·(-5)·8
Δ = 164
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:

$\sqrt{\Delta}=\sqrt{164}=\sqrt{4*41}=\sqrt{4}*\sqrt{41}=2\sqrt{41}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-2)-2\sqrt{41}}{2*-5}=\frac{2-2\sqrt{41}}{-10}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-2)+2\sqrt{41}}{2*-5}=\frac{2+2\sqrt{41}}{-10}
$