x^2+144=9x^2-12x+4

Solution for x^2+144=9x^2-12x+4 equation:

x^2+144=9x^2-12x+4

We move all terms to the left:

x^2+144-(9x^2-12x+4)=0

We get rid of parentheses

x^2-9x^2+12x-4+144=0

We add all the numbers together, and all the variables

-8x^2+12x+140=0

a = -8; b = 12; c = +140;
Δ = b2-4ac
Δ = 122-4·(-8)·140
Δ = 4624
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{4624}=68$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(12)-68}{2*-8}=\frac{-80}{-16}
=+5
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(12)+68}{2*-8}=\frac{56}{-16}
=-3+1/2
$