66x(x+7)=122

Solution for 66x(x+7)=122 equation:

66x(x+7)=122

We move all terms to the left:

66x(x+7)-(122)=0

We multiply parentheses

66x^2+462x-122=0

a = 66; b = 462; c = -122;
Δ = b2-4ac
Δ = 4622-4·66·(-122)
Δ = 245652
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:

$\sqrt{\Delta}=\sqrt{245652}=\sqrt{4*61413}=\sqrt{4}*\sqrt{61413}=2\sqrt{61413}$
$x_{1}=\frac{-b-\sqrt{\Delta}}{2a}=\frac{-(462)-2\sqrt{61413}}{2*66}=\frac{-462-2\sqrt{61413}}{132}
$
$x_{2}=\frac{-b+\sqrt{\Delta}}{2a}=\frac{-(462)+2\sqrt{61413}}{2*66}=\frac{-462+2\sqrt{61413}}{132}
$