14x-2x+3=3(5x+9)12x+3

Solution for 14x-2x+3=3(5x+9)12x+3 equation:

14x-2x+3=3(5x+9)12x+3

We move all terms to the left:

14x-2x+3-(3(5x+9)12x+3)=0

We add all the numbers together, and all the variables

12x-(3(5x+9)12x+3)+3=0


We calculate terms in parentheses: -(3(5x+9)12x+3), so:

3(5x+9)12x+3

We multiply parentheses

180x^2+324x+3

Back to the equation:

-(180x^2+324x+3)


We get rid of parentheses

-180x^2+12x-324x-3+3=0

We add all the numbers together, and all the variables

-180x^2-312x=0

a = -180; b = -312; c = 0;
Δ = b2-4ac
Δ = -3122-4·(-180)·0
Δ = 97344
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{97344}=312$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-312)-312}{2*-180}=\frac{0}{-360}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-312)+312}{2*-180}=\frac{624}{-360}
=-1+11/15
$