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

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
$