(2x+6)(x+7)-x^2=138

Solution for (2x+6)(x+7)-x^2=138 equation:

(2x+6)(x+7)-x^2=138

We move all terms to the left:

(2x+6)(x+7)-x^2-(138)=0

We add all the numbers together, and all the variables

-1x^2+(2x+6)(x+7)-138=0

We multiply parentheses ..

-1x^2+(+2x^2+14x+6x+42)-138=0

We get rid of parentheses

-1x^2+2x^2+14x+6x+42-138=0

We add all the numbers together, and all the variables

x^2+20x-96=0

a = 1; b = 20; c = -96;
Δ = b2-4ac
Δ = 202-4·1·(-96)
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{-(20)-28}{2*1}=\frac{-48}{2}
=-24
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(20)+28}{2*1}=\frac{8}{2}
=4
$