4x2-x=2x+27

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Solution for 4x2-x=2x+27 equation:



4x^2-x=2x+27
We move all terms to the left:
4x^2-x-(2x+27)=0
We add all the numbers together, and all the variables
4x^2-1x-(2x+27)=0
We get rid of parentheses
4x^2-1x-2x-27=0
We add all the numbers together, and all the variables
4x^2-3x-27=0
a = 4; b = -3; c = -27;
Δ = b2-4ac
Δ = -32-4·4·(-27)
Δ = 441
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{441}=21$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-3)-21}{2*4}=\frac{-18}{8} =-2+1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-3)+21}{2*4}=\frac{24}{8} =3 $

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