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

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

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

We move all terms to the left:

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

We multiply parentheses

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

We get rid of parentheses

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

We add all the numbers together, and all the variables

7x^2-10x-2=0

a = 7; b = -10; c = -2;
Δ = b2-4ac
Δ = -102-4·7·(-2)
Δ = 156
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

The end solution:

$\sqrt{\Delta}=\sqrt{156}=\sqrt{4*39}=\sqrt{4}*\sqrt{39}=2\sqrt{39}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-10)-2\sqrt{39}}{2*7}=\frac{10-2\sqrt{39}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-10)+2\sqrt{39}}{2*7}=\frac{10+2\sqrt{39}}{14}
$