(2X+38)(12x-54)=120

Solution for (2X+38)(12x-54)=120 equation:

(2X+38)(12X-54)=120

We move all terms to the left:

(2X+38)(12X-54)-(120)=0

We multiply parentheses ..

(+24X^2-108X+456X-2052)-120=0

We get rid of parentheses

24X^2-108X+456X-2052-120=0

We add all the numbers together, and all the variables

24X^2+348X-2172=0

a = 24; b = 348; c = -2172;
Δ = b2-4ac
Δ = 3482-4·24·(-2172)
Δ = 329616
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:

$\sqrt{\Delta}=\sqrt{329616}=\sqrt{144*2289}=\sqrt{144}*\sqrt{2289}=12\sqrt{2289}$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(348)-12\sqrt{2289}}{2*24}=\frac{-348-12\sqrt{2289}}{48}
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(348)+12\sqrt{2289}}{2*24}=\frac{-348+12\sqrt{2289}}{48}
$