4x2-3x-18=x2

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Solution for 4x2-3x-18=x2 equation:



4x^2-3x-18=x2
We move all terms to the left:
4x^2-3x-18-(x2)=0
We add all the numbers together, and all the variables
3x^2-3x-18=0
a = 3; b = -3; c = -18;
Δ = b2-4ac
Δ = -32-4·3·(-18)
Δ = 225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{225}=15$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-15}{2*3}=\frac{-12}{6} =-2 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+15}{2*3}=\frac{18}{6} =3 $

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