(3x-12)(4x+1)=0

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Solution for (3x-12)(4x+1)=0 equation:



(3x-12)(4x+1)=0
We multiply parentheses ..
(+12x^2+3x-48x-12)=0
We get rid of parentheses
12x^2+3x-48x-12=0
We add all the numbers together, and all the variables
12x^2-45x-12=0
a = 12; b = -45; c = -12;
Δ = b2-4ac
Δ = -452-4·12·(-12)
Δ = 2601
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{2601}=51$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-45)-51}{2*12}=\frac{-6}{24} =-1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-45)+51}{2*12}=\frac{96}{24} =4 $

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