3x-12=4/6x+15

Solution for 3x-12=4/6x+15 equation:

3x-12=4/6x+15

We move all terms to the left:

3x-12-(4/6x+15)=0


Domain of the equation: 6x+15)!=0

x∈R


We get rid of parentheses

3x-4/6x-15-12=0

We multiply all the terms by the denominator


3x*6x-15*6x-12*6x-4=0

Wy multiply elements

18x^2-90x-72x-4=0

We add all the numbers together, and all the variables

18x^2-162x-4=0

a = 18; b = -162; c = -4;
Δ = b2-4ac
Δ = -1622-4·18·(-4)
Δ = 26532
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:

$\sqrt{\Delta}=\sqrt{26532}=\sqrt{36*737}=\sqrt{36}*\sqrt{737}=6\sqrt{737}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-162)-6\sqrt{737}}{2*18}=\frac{162-6\sqrt{737}}{36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-162)+6\sqrt{737}}{2*18}=\frac{162+6\sqrt{737}}{36}
$