(X+7)(12x-27)=123

Solution for (X+7)(12x-27)=123 equation:

(X+7)(12X-27)=123

We move all terms to the left:

(X+7)(12X-27)-(123)=0

We multiply parentheses ..

(+12X^2-27X+84X-189)-123=0

We get rid of parentheses

12X^2-27X+84X-189-123=0

We add all the numbers together, and all the variables

12X^2+57X-312=0

a = 12; b = 57; c = -312;
Δ = b2-4ac
Δ = 572-4·12·(-312)
Δ = 18225
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{18225}=135$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(57)-135}{2*12}=\frac{-192}{24}
=-8
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(57)+135}{2*12}=\frac{78}{24}
=3+1/4
$