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

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

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

We move all terms to the left:

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

We add all the numbers together, and all the variables

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

We multiply parentheses

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

We add all the numbers together, and all the variables

7x^2-12x-4=0

a = 7; b = -12; c = -4;
Δ = b2-4ac
Δ = -122-4·7·(-4)
Δ = 256
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{256}=16$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-12)-16}{2*7}=\frac{-4}{14}
=-2/7
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-12)+16}{2*7}=\frac{28}{14}
=2
$