3x+3=51/12x+12=15

Solution for 3x+3=51/12x+12=15 equation:

3x+3=51/12x+12=15

We move all terms to the left:

3x+3-(51/12x+12)=0


Domain of the equation: 12x+12)!=0

x∈R


We get rid of parentheses

3x-51/12x-12+3=0

We multiply all the terms by the denominator


3x*12x-12*12x+3*12x-51=0

Wy multiply elements

36x^2-144x+36x-51=0

We add all the numbers together, and all the variables

36x^2-108x-51=0

a = 36; b = -108; c = -51;
Δ = b2-4ac
Δ = -1082-4·36·(-51)
Δ = 19008
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:

$\sqrt{\Delta}=\sqrt{19008}=\sqrt{576*33}=\sqrt{576}*\sqrt{33}=24\sqrt{33}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-108)-24\sqrt{33}}{2*36}=\frac{108-24\sqrt{33}}{72}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-108)+24\sqrt{33}}{2*36}=\frac{108+24\sqrt{33}}{72}
$