F(x)=3x2+5x-10

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Solution for F(x)=3x2+5x-10 equation:



(F)=3F^2+5F-10
We move all terms to the left:
(F)-(3F^2+5F-10)=0
We get rid of parentheses
-3F^2+F-5F+10=0
We add all the numbers together, and all the variables
-3F^2-4F+10=0
a = -3; b = -4; c = +10;
Δ = b2-4ac
Δ = -42-4·(-3)·10
Δ = 136
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:
$\sqrt{\Delta}=\sqrt{136}=\sqrt{4*34}=\sqrt{4}*\sqrt{34}=2\sqrt{34}$
$F_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-2\sqrt{34}}{2*-3}=\frac{4-2\sqrt{34}}{-6} $
$F_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+2\sqrt{34}}{2*-3}=\frac{4+2\sqrt{34}}{-6} $

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