7x(x-1)=2-3

Solution for 7x(x-1)=2-3 equation:

7x(x-1)=2-3

We move all terms to the left:

7x(x-1)-(2-3)=0

We add all the numbers together, and all the variables

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

We add all the numbers together, and all the variables

7x(x-1)+1=0

We multiply parentheses

7x^2-7x+1=0

a = 7; b = -7; c = +1;
Δ = b2-4ac
Δ = -72-4·7·1
Δ = 21
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-7)-\sqrt{21}}{2*7}=\frac{7-\sqrt{21}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-7)+\sqrt{21}}{2*7}=\frac{7+\sqrt{21}}{14}
$