(x-2)(3+7x)=-6

Solution for (x-2)(3+7x)=-6 equation:

(x-2)(3+7x)=-6

We move all terms to the left:

(x-2)(3+7x)-(-6)=0

We add all the numbers together, and all the variables

(x-2)(7x+3)-(-6)=0

We add all the numbers together, and all the variables

(x-2)(7x+3)+6=0

We multiply parentheses ..

(+7x^2+3x-14x-6)+6=0

We get rid of parentheses

7x^2+3x-14x-6+6=0

We add all the numbers together, and all the variables

7x^2-11x=0

a = 7; b = -11; c = 0;
Δ = b2-4ac
Δ = -112-4·7·0
Δ = 121
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{121}=11$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-11)-11}{2*7}=\frac{0}{14}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-11)+11}{2*7}=\frac{22}{14}
=1+4/7
$