3x(x-7)=21

Solution for 3x(x-7)=21 equation:

3x(x-7)=21

We move all terms to the left:

3x(x-7)-(21)=0

We multiply parentheses

3x^2-21x-21=0

a = 3; b = -21; c = -21;
Δ = b2-4ac
Δ = -212-4·3·(-21)
Δ = 693
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:

$\sqrt{\Delta}=\sqrt{693}=\sqrt{9*77}=\sqrt{9}*\sqrt{77}=3\sqrt{77}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-3\sqrt{77}}{2*3}=\frac{21-3\sqrt{77}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+3\sqrt{77}}{2*3}=\frac{21+3\sqrt{77}}{6}
$