(X+6)(3X-2)-(x-1)(2X)=103

Solution for (X+6)(3X-2)-(x-1)(2X)=103 equation:

(X+6)(3X-2)-(X-1)(2X)=103

We move all terms to the left:

(X+6)(3X-2)-(X-1)(2X)-(103)=0

We multiply parentheses

-2X^2+(X+6)(3X-2)+2X-103=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

X^2+18X-115=0

a = 1; b = 18; c = -115;
Δ = b2-4ac
Δ = 182-4·1·(-115)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$X_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(18)-28}{2*1}=\frac{-46}{2}
=-23
$
$X_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(18)+28}{2*1}=\frac{10}{2}
=5
$