14x^2-3x-12=9x^2+4x

Solution for 14x^2-3x-12=9x^2+4x equation:

14x^2-3x-12=9x^2+4x

We move all terms to the left:

14x^2-3x-12-(9x^2+4x)=0

We get rid of parentheses

14x^2-9x^2-3x-4x-12=0

We add all the numbers together, and all the variables

5x^2-7x-12=0

a = 5; b = -7; c = -12;
Δ = b2-4ac
Δ = -72-4·5·(-12)
Δ = 289
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{289}=17$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-17}{2*5}=\frac{-10}{10}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+17}{2*5}=\frac{24}{10}
=2+2/5
$