3(12^2+x+1)+12(12x^2+x+1)=15(12x^2+x+1)

Solution for 3(12^2+x+1)+12(12x^2+x+1)=15(12x^2+x+1) equation:

3(12^2+x+1)+12(12x^2+x+1)=15(12x^2+x+1)

We move all terms to the left:

3(12^2+x+1)+12(12x^2+x+1)-(15(12x^2+x+1))=0

We multiply parentheses

144x^2+3x+12x-(15(12x^2+x+1))+432+3+12=0


We calculate terms in parentheses: -(15(12x^2+x+1)), so:

15(12x^2+x+1)

We multiply parentheses

180x^2+15x+15

Back to the equation:

-(180x^2+15x+15)


We add all the numbers together, and all the variables

144x^2+15x-(180x^2+15x+15)+447=0

We get rid of parentheses

144x^2-180x^2+15x-15x-15+447=0

We add all the numbers together, and all the variables

-36x^2+432=0

a = -36; b = 0; c = +432;
Δ = b2-4ac
Δ = 02-4·(-36)·432
Δ = 62208
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:

$\sqrt{\Delta}=\sqrt{62208}=\sqrt{20736*3}=\sqrt{20736}*\sqrt{3}=144\sqrt{3}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(0)-144\sqrt{3}}{2*-36}=\frac{0-144\sqrt{3}}{-72}
=-\frac{144\sqrt{3}}{-72}
=-\frac{2\sqrt{3}}{-1}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(0)+144\sqrt{3}}{2*-36}=\frac{0+144\sqrt{3}}{-72}
=\frac{144\sqrt{3}}{-72}
=\frac{2\sqrt{3}}{-1}
$