(14-3x)(12-2x)=120

Solution for (14-3x)(12-2x)=120 equation:

(14-3x)(12-2x)=120

We move all terms to the left:

(14-3x)(12-2x)-(120)=0

We add all the numbers together, and all the variables

(-3x+14)(-2x+12)-120=0

We multiply parentheses ..

(+6x^2-36x-28x+168)-120=0

We get rid of parentheses

6x^2-36x-28x+168-120=0

We add all the numbers together, and all the variables

6x^2-64x+48=0

a = 6; b = -64; c = +48;
Δ = b2-4ac
Δ = -642-4·6·48
Δ = 2944
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:

$\sqrt{\Delta}=\sqrt{2944}=\sqrt{64*46}=\sqrt{64}*\sqrt{46}=8\sqrt{46}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-64)-8\sqrt{46}}{2*6}=\frac{64-8\sqrt{46}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-64)+8\sqrt{46}}{2*6}=\frac{64+8\sqrt{46}}{12}
$