2x+12=3/4x+27

Solution for 2x+12=3/4x+27 equation:

2x+12=3/4x+27

We move all terms to the left:

2x+12-(3/4x+27)=0


Domain of the equation: 4x+27)!=0

x∈R


We get rid of parentheses

2x-3/4x-27+12=0

We multiply all the terms by the denominator


2x*4x-27*4x+12*4x-3=0

Wy multiply elements

8x^2-108x+48x-3=0

We add all the numbers together, and all the variables

8x^2-60x-3=0

a = 8; b = -60; c = -3;
Δ = b2-4ac
Δ = -602-4·8·(-3)
Δ = 3696
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:

$\sqrt{\Delta}=\sqrt{3696}=\sqrt{16*231}=\sqrt{16}*\sqrt{231}=4\sqrt{231}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-60)-4\sqrt{231}}{2*8}=\frac{60-4\sqrt{231}}{16}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-60)+4\sqrt{231}}{2*8}=\frac{60+4\sqrt{231}}{16}
$