F(x)=2.15(2x2-4x-6)

Solution for F(x)=2.15(2x2-4x-6) equation:

(F)=2.15(2F^2-4F-6)

We move all terms to the left:

(F)-(2.15(2F^2-4F-6))=0


We calculate terms in parentheses: -(2.15(2F^2-4F-6)), so:

2.15(2F^2-4F-6)

We multiply parentheses

4.3F^2-8.6F-12.9

Back to the equation:

-(4.3F^2-8.6F-12.9)


We get rid of parentheses

-4.3F^2+F+8.6F+12.9=0

We add all the numbers together, and all the variables

-4.3F^2+9.6F+12.9=0

a = -4.3; b = 9.6; c = +12.9;
Δ = b2-4ac
Δ = 9.62-4·(-4.3)·12.9
Δ = 314.04
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{-(9.6)-\sqrt{314.04}}{2*-4.3}=\frac{-9.6-\sqrt{314.04}}{-8.6}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(9.6)+\sqrt{314.04}}{2*-4.3}=\frac{-9.6+\sqrt{314.04}}{-8.6}
$