7x(x-2)=21

Solution for 7x(x-2)=21 equation:

7x(x-2)=21

We move all terms to the left:

7x(x-2)-(21)=0

We multiply parentheses

7x^2-14x-21=0

a = 7; b = -14; c = -21;
Δ = b2-4ac
Δ = -142-4·7·(-21)
Δ = 784
The delta value is higher than zero, so the equation has two solutions
We use following formulas to calculate our solutions:
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}$

$\sqrt{\Delta}=\sqrt{784}=28$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-14)-28}{2*7}=\frac{-14}{14}
=-1
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-14)+28}{2*7}=\frac{42}{14}
=3
$