(3x-2)(x+6)=103

Solution for (3x-2)(x+6)=103 equation:

(3x-2)(x+6)=103

We move all terms to the left:

(3x-2)(x+6)-(103)=0

We multiply parentheses ..

(+3x^2+18x-2x-12)-103=0

We get rid of parentheses

3x^2+18x-2x-12-103=0

We add all the numbers together, and all the variables

3x^2+16x-115=0

a = 3; b = 16; c = -115;
Δ = b2-4ac
Δ = 162-4·3·(-115)
Δ = 1636
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:

$\sqrt{\Delta}=\sqrt{1636}=\sqrt{4*409}=\sqrt{4}*\sqrt{409}=2\sqrt{409}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(16)-2\sqrt{409}}{2*3}=\frac{-16-2\sqrt{409}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(16)+2\sqrt{409}}{2*3}=\frac{-16+2\sqrt{409}}{6}
$