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

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

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

We move all terms to the left:

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3F^2-7F+5=0

a = -3; b = -7; c = +5;
Δ = b2-4ac
Δ = -72-4·(-3)·5
Δ = 109
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{-(-7)-\sqrt{109}}{2*-3}=\frac{7-\sqrt{109}}{-6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{109}}{2*-3}=\frac{7+\sqrt{109}}{-6}
$