4x(x-3)+2x=27

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Solution for 4x(x-3)+2x=27 equation:



4x(x-3)+2x=27
We move all terms to the left:
4x(x-3)+2x-(27)=0
We add all the numbers together, and all the variables
2x+4x(x-3)-27=0
We multiply parentheses
4x^2+2x-12x-27=0
We add all the numbers together, and all the variables
4x^2-10x-27=0
a = 4; b = -10; c = -27;
Δ = b2-4ac
Δ = -102-4·4·(-27)
Δ = 532
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:
$\sqrt{\Delta}=\sqrt{532}=\sqrt{4*133}=\sqrt{4}*\sqrt{133}=2\sqrt{133}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{133}}{2*4}=\frac{10-2\sqrt{133}}{8} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{133}}{2*4}=\frac{10+2\sqrt{133}}{8} $

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