(4x+1)*3x/2=27

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Solution for (4x+1)*3x/2=27 equation:



(4x+1)*3x/2=27
We move all terms to the left:
(4x+1)*3x/2-(27)=0
We multiply all the terms by the denominator
(4x+1)*3x-27*2=0
We add all the numbers together, and all the variables
(4x+1)*3x-54=0
We multiply parentheses
12x^2+3x-54=0
a = 12; b = 3; c = -54;
Δ = b2-4ac
Δ = 32-4·12·(-54)
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{-(3)-51}{2*12}=\frac{-54}{24} =-2+1/4 $
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+51}{2*12}=\frac{48}{24} =2 $

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