12/3x+7=6x+15

Solution for 12/3x+7=6x+15 equation:

12/3x+7=6x+15

We move all terms to the left:

12/3x+7-(6x+15)=0


Domain of the equation: 3x!=0

x!=0/3

x!=0

x∈R


We get rid of parentheses

12/3x-6x-15+7=0

We multiply all the terms by the denominator


-6x*3x-15*3x+7*3x+12=0

Wy multiply elements

-18x^2-45x+21x+12=0

We add all the numbers together, and all the variables

-18x^2-24x+12=0

a = -18; b = -24; c = +12;
Δ = b2-4ac
Δ = -242-4·(-18)·12
Δ = 1440
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:

$\sqrt{\Delta}=\sqrt{1440}=\sqrt{144*10}=\sqrt{144}*\sqrt{10}=12\sqrt{10}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-24)-12\sqrt{10}}{2*-18}=\frac{24-12\sqrt{10}}{-36}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-24)+12\sqrt{10}}{2*-18}=\frac{24+12\sqrt{10}}{-36}
$