(6x+7)(x+1)=26

Solution for (6x+7)(x+1)=26 equation:

(6x+7)(x+1)=26

We move all terms to the left:

(6x+7)(x+1)-(26)=0

We multiply parentheses ..

(+6x^2+6x+7x+7)-26=0

We get rid of parentheses

6x^2+6x+7x+7-26=0

We add all the numbers together, and all the variables

6x^2+13x-19=0

a = 6; b = 13; c = -19;
Δ = b2-4ac
Δ = 132-4·6·(-19)
Δ = 625
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{625}=25$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(13)-25}{2*6}=\frac{-38}{12}
=-3+1/6
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(13)+25}{2*6}=\frac{12}{12}
=1
$