(4x-2)(3x+18)=120

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Solution for (4x-2)(3x+18)=120 equation:



(4x-2)(3x+18)=120
We move all terms to the left:
(4x-2)(3x+18)-(120)=0
We multiply parentheses ..
(+12x^2+72x-6x-36)-120=0
We get rid of parentheses
12x^2+72x-6x-36-120=0
We add all the numbers together, and all the variables
12x^2+66x-156=0
a = 12; b = 66; c = -156;
Δ = b2-4ac
Δ = 662-4·12·(-156)
Δ = 11844
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:
$\sqrt{\Delta}=\sqrt{11844}=\sqrt{36*329}=\sqrt{36}*\sqrt{329}=6\sqrt{329}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(66)-6\sqrt{329}}{2*12}=\frac{-66-6\sqrt{329}}{24} $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(66)+6\sqrt{329}}{2*12}=\frac{-66+6\sqrt{329}}{24} $

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