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

Solution for (-7x+3)(x-1)=0 equation:

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

We multiply parentheses ..

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

-7x^2+10x-3=0

a = -7; b = 10; c = -3;
Δ = b2-4ac
Δ = 102-4·(-7)·(-3)
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{-(10)-4}{2*-7}=\frac{-14}{-14}
=1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(10)+4}{2*-7}=\frac{-6}{-14}
=3/7
$