7x(x-6)=28

Solution for 7x(x-6)=28 equation:

7x(x-6)=28

We move all terms to the left:

7x(x-6)-(28)=0

We multiply parentheses

7x^2-42x-28=0

a = 7; b = -42; c = -28;
Δ = b2-4ac
Δ = -422-4·7·(-28)
Δ = 2548
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:

$\sqrt{\Delta}=\sqrt{2548}=\sqrt{196*13}=\sqrt{196}*\sqrt{13}=14\sqrt{13}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(-42)-14\sqrt{13}}{2*7}=\frac{42-14\sqrt{13}}{14}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(-42)+14\sqrt{13}}{2*7}=\frac{42+14\sqrt{13}}{14}
$