(3x-1)(2x+3)=124

Solution for (3x-1)(2x+3)=124 equation:

(3x-1)(2x+3)=124

We move all terms to the left:

(3x-1)(2x+3)-(124)=0

We multiply parentheses ..

(+6x^2+9x-2x-3)-124=0

We get rid of parentheses

6x^2+9x-2x-3-124=0

We add all the numbers together, and all the variables

6x^2+7x-127=0

a = 6; b = 7; c = -127;
Δ = b2-4ac
Δ = 72-4·6·(-127)
Δ = 3097
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{-(7)-\sqrt{3097}}{2*6}=\frac{-7-\sqrt{3097}}{12}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(7)+\sqrt{3097}}{2*6}=\frac{-7+\sqrt{3097}}{12}
$