F(x)=2x^2-13x+15F(-2)

Solution for F(x)=2x^2-13x+15F(-2) equation:

(F)=2F^2-13F+15(-2)

We move all terms to the left:

(F)-(2F^2-13F+15(-2))=0


We calculate terms in parentheses: -(2F^2-13F+15(-2)), so:

2F^2-13F+15(-2)

We add all the numbers together, and all the variables

2F^2-13F-30

Back to the equation:

-(2F^2-13F-30)


We get rid of parentheses

-2F^2+F+13F+30=0

We add all the numbers together, and all the variables

-2F^2+14F+30=0

a = -2; b = 14; c = +30;
Δ = b2-4ac
Δ = 142-4·(-2)·30
Δ = 436
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:

$\sqrt{\Delta}=\sqrt{436}=\sqrt{4*109}=\sqrt{4}*\sqrt{109}=2\sqrt{109}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(14)-2\sqrt{109}}{2*-2}=\frac{-14-2\sqrt{109}}{-4}
$
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(14)+2\sqrt{109}}{2*-2}=\frac{-14+2\sqrt{109}}{-4}
$