(-1x+1)(3x+7)=7

Solution for (-1x+1)(3x+7)=7 equation:

(-1x+1)(3x+7)=7

We move all terms to the left:

(-1x+1)(3x+7)-(7)=0

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-3x^2-4x=0

a = -3; b = -4; c = 0;
Δ = b2-4ac
Δ = -42-4·(-3)·0
Δ = 16
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{16}=4$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-4)-4}{2*-3}=\frac{0}{-6}
=0
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-4)+4}{2*-3}=\frac{8}{-6}
=-1+1/3
$