F(x)=2x(2)+5x-17

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Solution for F(x)=2x(2)+5x-17 equation:



(F)=2F(2)+5F-17
We move all terms to the left:
(F)-(2F(2)+5F-17)=0
We add all the numbers together, and all the variables
-(+2F^2+5F-17)+F=0
We get rid of parentheses
-2F^2-5F+F+17=0
We add all the numbers together, and all the variables
-2F^2-4F+17=0
a = -2; b = -4; c = +17;
Δ = b2-4ac
Δ = -42-4·(-2)·17
Δ = 152
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:
$\sqrt{\Delta}=\sqrt{152}=\sqrt{4*38}=\sqrt{4}*\sqrt{38}=2\sqrt{38}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{38}}{2*-2}=\frac{4-2\sqrt{38}}{-4} $
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{38}}{2*-2}=\frac{4+2\sqrt{38}}{-4} $

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