14-4+12x-9x+12x^2=14x^2-12

Solution for 14-4+12x-9x+12x^2=14x^2-12 equation:

14-4+12x-9x+12x^2=14x^2-12

We move all terms to the left:

14-4+12x-9x+12x^2-(14x^2-12)=0

We add all the numbers together, and all the variables

12x^2+3x-(14x^2-12)+10=0

We get rid of parentheses

12x^2-14x^2+3x+12+10=0

We add all the numbers together, and all the variables

-2x^2+3x+22=0

a = -2; b = 3; c = +22;
Δ = b2-4ac
Δ = 32-4·(-2)·22
Δ = 185
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(3)-\sqrt{185}}{2*-2}=\frac{-3-\sqrt{185}}{-4}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(3)+\sqrt{185}}{2*-2}=\frac{-3+\sqrt{185}}{-4}
$