3x=-5/6x-12

Solution for 3x=-5/6x-12 equation:

3x=-5/6x-12

We move all terms to the left:

3x-(-5/6x-12)=0


Domain of the equation: 6x-12)!=0

x∈R


We get rid of parentheses

3x+5/6x+12=0

We multiply all the terms by the denominator


3x*6x+12*6x+5=0

Wy multiply elements

18x^2+72x+5=0

a = 18; b = 72; c = +5;
Δ = b2-4ac
Δ = 722-4·18·5
Δ = 4824
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:

$\sqrt{\Delta}=\sqrt{4824}=\sqrt{36*134}=\sqrt{36}*\sqrt{134}=6\sqrt{134}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(72)-6\sqrt{134}}{2*18}=\frac{-72-6\sqrt{134}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(72)+6\sqrt{134}}{2*18}=\frac{-72+6\sqrt{134}}{36}
$