3x(x-7)=82

Solution for 3x(x-7)=82 equation:

3x(x-7)=82

We move all terms to the left:

3x(x-7)-(82)=0

We multiply parentheses

3x^2-21x-82=0

a = 3; b = -21; c = -82;
Δ = b2-4ac
Δ = -212-4·3·(-82)
Δ = 1425
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:

$\sqrt{\Delta}=\sqrt{1425}=\sqrt{25*57}=\sqrt{25}*\sqrt{57}=5\sqrt{57}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-21)-5\sqrt{57}}{2*3}=\frac{21-5\sqrt{57}}{6}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-21)+5\sqrt{57}}{2*3}=\frac{21+5\sqrt{57}}{6}
$